A garment multi-process digital twin monitoring method

Abstract

The present application relates to the technical field of intelligent manufacturing and production scheduling, and particularly relates to a garment multi-process digital twin monitoring method, which comprises the following steps: establishing a process digital twin by using a colored time-delay Petri network and an event dictionary; hierarchically updating a processing time distribution and a line change cost matrix online; obtaining a coupling matrix and calculating a dual price vector by using a regularized optimal transport, and quantifying a work-in-process capacity upper limit as a work-in-process quota; calling a Koopman operator driven counterfactual generator to evaluate an incremental cost and generate a release sequence by optimal sorting within a rolling prediction window; locking and issuing a process path according to the quota, implementing a reversible fine-tuning based on a deviation, and triggering a withdrawal and path diversion according to a topological structure abstract. The present application reduces work-in-process peak value and line change loss, and improves production capacity utilization and stability of on-time delivery.

Description

Technical Field

[0001] This invention relates to the field of intelligent manufacturing and production scheduling technology, and in particular to a digital twin monitoring method for multiple processes in garment manufacturing. Background Technology

[0002] The garment manufacturing industry is characterized by small batches, multiple product categories, short lead times, and frequent line changes. Parallel processes, rework, and equipment collaboration lead to highly unstable work-in-process distribution and capacity utilization. The significance of multi-process digital twin monitoring lies in connecting monitoring and scheduling with a unified process semantics: accurately representing work-in-process location, queue evolution, line changeover impact, and capacity capacity within the same model. This allows release and rearrangement to operate in a closed loop based on calculable, verifiable, and auditable constraints and indicators, reducing work-in-process peaks, minimizing ineffective line changes and delays, and stabilizing delivery rhythm. Summary of the Invention

[0003] To address the numerous problems existing in the prior art, this invention provides a solution that uses a colored delay Petri net to carry a process digital twin, event-driven hierarchical online assimilation, regularized optimal transmission to align demand and capacity, and generates a dual price vector and work-in-process quota. Combined with Koopman operator counterfactual evaluation and topology summary triggering mechanism, it completes executable release, reversible fine-tuning, and path rerouting, reducing work-in-process and line-changing losses, and ensuring stable delivery.

[0004] A digital twin monitoring method for multiple processes in garment manufacturing includes the following steps:

[0005] A process digital twin represented by a colored time-delay Petri net is established, and production signals are mapped to event streams according to a unified event dictionary. The initial state is determined by event playback and the line change cost matrix is ​​estimated accordingly.

[0006] Hierarchical online assimilation of event flow is performed to update processing time distribution and line change cost matrix. A topology summary is generated based on work-in-process flow graph. Predicted arrival flow and capacity carrying capacity distribution are constructed and the coupling matrix is ​​solved by regularized optimal transmission. Koopman operator is identified to form counterfactual generator.

[0007] Within the rolling prediction window, the dual price vector is calculated based on the assimilated processing time distribution, the line change cost matrix, and the coupling matrix. The upper limit of the work-in-process capacity is quantified into the work-in-process quota. The counterfactual generator is called to evaluate the incremental cost of batch release and rearrangement and to generate a release sequence by prioritizing the best results.

[0008] The process path is locked and issued based on the work-in-process quota, reversible fine-tuning is implemented based on the deviation between the expected state and the execution state, and withdrawal and path rerouting are triggered based on the topology summary.

[0009] Preferably, the determination of the initial state adopts the consistency check of event playback and place invariant to ensure that the process digital twin and the event flow maintain the conservation consistency in the number of tags and the direction of flow.

[0010] Preferably, the hierarchical online assimilation updates parameters at the equipment, workstation, product, and batch levels, and applies robust weighting to anomaly observations in the event flow to suppress the offset of the processing time distribution and changeover cost matrix.

[0011] Preferably, the topology summary is obtained by persistent cohomology calculation of the product flow graph and topology changes are measured by the bottleneck distance between adjacent time windows, which is used to trigger withdrawals and path rerouting.

[0012] Preferably, the cost matrix of the regularized optimal transmission is composed of a weighted average of the product attribute difference metric and the normalized value of the line-changing cost matrix, and the coupling matrix is ​​solved by Sinkhorn iteration.

[0013] Preferably, the identification of the Koopman operator is based on the observable function mapping of the state vector, which includes a polynomial expansion of the product position, queue length, equipment state and attribute pairs before and after line change, and the stability of the counterfactual generator is guaranteed by the spectral radius constraint.

[0014] Preferably, the dual price vector is updated using the sub-gradient rule and spatially smoothed using a graph Laplace constructed based on the coupling matrix. Temporal smoothing is performed on the dual price vector of adjacent periods when the capacity carrying capacity distribution changes little.

[0015] Preferably, when the upper limit of work-in-process capacity is quantified as work-in-process quota, the work-in-process quota is allocated according to bottlenecks and time periods, atomic locking is implemented for process paths that cross multiple bottlenecks, and the corresponding work-in-process quota is released according to the path after the operation is completed.

[0016] Preferably, the incremental cost is weighted by the product of the dual price and the change in work-in-process, the incremental cost of line switching, the incremental cost of delay, and the structural penalty term based on the topology summary. A two-level evaluation process is adopted, in which the first level is a fast evaluation based on the Koopman operator, and the second level is a short-window discrete event simulation refinement evaluation.

[0017] Preferably, reversible fine-tuning includes batch swapping and inbound delay operations for batches that have not yet started. The triggering conditions for withdrawal and route rerouting are that the structural indicators of the topology summary exceed a threshold. Route rerouting selects an alternative route from the set of feasible process routes based on the principle of minimizing incremental cost.

[0018] Compared with the prior art, the advantages and beneficial effects of the present invention are as follows:

[0019] By using colored delay Petri nets and a unified event dictionary to model process semantics, we achieved a consistent representation of the impact of work-in-process, queues, and line switching.

[0020] By updating the processing time distribution and line change cost matrix in a hierarchical online assimilation manner, the parameters were dynamically converged as the field conditions changed.

[0021] By constructing a coupling matrix through regularized optimal transmission, the distribution layer of demand distribution and capacity carrying capacity is aligned.

[0022] By calculating the dual price vector, continuous quantification and comparable pricing of congestion intensity are achieved.

[0023] By using workpiece quotas and atomic locking, a capacity constraint that can be executed once across bottleneck paths is achieved.

[0024] By using the Koopman operator and counterfactual generator, a fast incremental evaluation of candidate release and rearrangement is achieved.

[0025] By triggering withdrawals and path rerouting through topology summaries, structural solutions to ring congestion are achieved.

[0026] By using a rolling prediction window for optimal sorting and issuing release sequences, stable release and an auditable closed loop are achieved. Attached Figure Description

[0027] Figure 1 This is a flowchart illustrating the method of the present invention. Detailed Implementation

[0028] The embodiments of the present disclosure will now be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the disclosure. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of the present disclosure for ease of explanation.

[0029] like Figure 1 As shown, a digital twin monitoring method for multiple processes in garment manufacturing includes the following steps:

[0030] A process digital twin represented by a colored time-delay Petri net is established, and production signals are mapped to event streams according to a unified event dictionary. The initial state is determined by event playback and the line change cost matrix is ​​estimated accordingly.

[0031] The process digital twin uses colored time-delayed Petri nets as the semantic carrier for the process. Places represent each process and buffer location, transitions represent events such as arrival, start-up, completion, and line changeover, and tags carry color attribute vectors to describe product identification, size, color, fabric, accessory combinations, and process path identification. Delays are used to express processing time and line changeover duration. Through this representation, production status, work-in-process materials, and equipment occupancy are uniformly characterized within the same discrete event model, facilitating subsequent assimilation, prediction, and control.

[0032] The event dictionary is used to standardize production signals into an event stream. Barcode and RFID entry is recorded as arrival; barcode and RFID exit or manufacturing execution system (MES) reporting is recorded as completion; workstation start button or program initiation is recorded as start; workstation reporting confirmation or program termination is recorded as completion; equipment shutdown and recovery are recorded as shutdown and recovery respectively; operation panel cutting start and completion are recorded as line change start and line change end respectively. The event stream includes fields such as timestamp, equipment identifier, workstation identifier, process number, batch number, product identifier, and color attribute vector. To ensure time consistency, a unified time synchronization and late event window strategy are adopted. Late events are reordered within the window; events exceeding the window enter a compensation queue and are corrected in the next cycle without disrupting the submitted state.

[0033] The initial state progresses from the most recent timestamp to the current time through event replay. Core updates follow the expression below:

[0034] ,

[0035] in, Indicates time The tag vector contains the number of work-in-process items in each repository; This represents an association matrix, where rows correspond to locations and columns correspond to migrations. Indicates at time The triggered transition vector has elements of either 0 or 1. The initial state is obtained by sequentially triggering events on the timeline and updating the marker vector. The initial state includes attribute pairs related to work-in-progress distribution, queue length, equipment availability, and pre- and post-change attributes. To avoid modeling drift, a structural consistency check is introduced. The place invariant is used to verify conservation relationships, and when inconsistencies are found, the event segment with the least impact is replayed and repaired.

[0036] The changeover cost matrix measures the time and energy consumption of switching from one attribute combination to another. Without changing process path constraints, the changeover cost is modeled as a weighted sum of attribute differences, allowing for attribute interactions.

[0037] ,

[0038] in, and These represent attribute vectors before and after the line change, with components corresponding to color, fabric, size, and accessory combinations, etc. Indicates the first An indicator of whether an attribute has changed, taking the value 0 or 1; Indicates the first and The indicator for whether the second attribute changes simultaneously is either 0 or 1. The parameters to be identified are defined as follows. Parameter identification employs a least squares method with non-negativity constraints and robust weights for outlier samples. Training samples consist of the duration from "line change start" to "line change end" and the corresponding attribute pairs. To improve transferability, shared priors are established for different devices, and constraints are applied at the device level, ensuring stable estimations even for workstations with sparse samples. Energy consumption can be modeled in parallel with the same structure for use in energy efficiency analysis and line change direction penalties.

[0039] The application path of this invention is as follows: First, the process digital twin carries the mutual exclusion relationships of processes, buffers, and equipment, enabling work-in-process flow and resource occupation to have computable event semantics; second, the event dictionary normalizes heterogeneous signals into an event stream, ensuring that event replay can reproduce the real production trajectory; third, a reliable initial state is obtained through event replay, which serves as the starting point for subsequent assimilation and prediction; finally, the changeover cost matrix establishes a connection between the product attribute space and equipment switching costs, providing quantifiable marginal costs for subsequent release sequencing, path selection, and changeover direction determination. Thus, the monitoring layer can simultaneously display the work-in-process position, queue changes, and potential changeover costs within a single model, and the scheduling layer can quickly assess the impact of release and rearrangement based on the initial state.

[0040] Compared to solutions relying solely on empirical rules or single signals, this step is effective in three ways. First, state consistency: through event playback and structural consistency verification, the initial state corresponds one-to-one with the actual production records, avoiding misjudgments caused by state drift. Second, interpretable costs: the line change cost matrix uses attribute differences as independent variables, and the coefficients have clear physical meanings, facilitating auditing and maintenance. Third, cross-line migration: through hierarchical constraints and robust identification of parameters, the model can migrate between different equipment and workstations, reducing the cost of repeated calibration.

[0041] Example: A production line including cutting, sewing, ironing, and final inspection is selected as the object. In the process digital twin, the cutting exit, sewing entrance, sewing buffer, thread change resource position, ironing station, and final inspection position are all set as warehouses, and arrival, start, completion, thread change start, and thread change end are set as transitions. The event dictionary defines barcode scanning entry as arrival, work reporting and barcode exit as completion, station start / stop buttons as start and completion, and cutting commands on the operation panel as thread change start and thread change end. The event stream within one shift is collected and timed and late corrections are performed. Then, event playback is executed, and the initial state is obtained using the aforementioned update expression. The work-in-process distribution shows that the work-in-process in the sewing buffer is higher than that at the ironing entrance. Based on the same data, attribute pairs of all thread change segments are extracted. The attribute dimensions include color, fabric, and size. A robust weighted least squares method is used to identify the thread change cost matrix parameters, and non-negativity constraints are applied. The identification results show that the weight of color changes is higher than that of size changes, and the weight of interaction items where both color and fabric change simultaneously is higher than the sum of their individual weights. This matrix is ​​applied to a monitoring dashboard to calculate the time cost of candidate releases and potential line-changing directions in real time, which is used for subsequent priority assessment and path selection. In subsequent rolling cycles, the initial state serves as the starting point for the assimilation and prediction process. The line-changing cost matrix is ​​updated incrementally in small steps as new samples arrive, ensuring that the cost assessment is consistent with the actual situation.

[0042] Preferably, the determination of the initial state adopts the consistency check of event playback and place invariant to ensure that the process digital twin and the event flow maintain the conservation consistency in the number of tags and the direction of flow.

[0043] The process digital twin uses colored time-delay Petri nets to represent the relationships between processes, buffers, and equipment occupancy. The event replay principle is based on event time sequence, triggering arrival, start-up, completion, changeover start, and changeover end one by one to the corresponding transition, driving the migration of markers between warehouses and reconstructing the current distribution of work-in-process and queues. The core update follows a marker-update formula:

[0044] ,

[0045] in, For a moment The tag vector (the number of work-in-process items in each repository). It is an association matrix (rows correspond to locations, columns correspond to migration). For a moment The triggered transition vector (elements are either 0 or 1). To avoid repeated rollbacks due to out-of-order timing, event time watermarking and a late window are used. Late events within the window are placed in a local replay queue, while late events outside the window enter a compensation queue to await processing in the next cycle. The place invariant consistency check is used to constrain the replay results at the structural level. If a vector exists... satisfy:

[0046] ,

[0047] Then, for any triggering sequence, the conservation relationship holds:

[0048] ,

[0049] in, This is a vector of invariant values ​​for each warehouse, where each element represents a weighted summation coefficient for each warehouse. In practice, a set of base invariant vectors is derived offline from the process diagram. The above conservation is verified one by one for each marker vector after each partial replay. If a deviation occurs, the deviation component is recorded, and the smallest event segment causing the deviation is located. Priority is given to backtracking and deleting duplicate events, correcting cross-equipment mismatches, or merging broken line-changing segments. The replay is then repeated until the deviation is eliminated. This process ensures the structural correctness of "counting and flow direction," making the initial state auditable.

[0050] After the initial state calculation is completed, the work-in-process distribution, entry queues for each process, equipment availability, and attribute pairs before and after line changeover are obtained. The attribute pairs and durations in the attribute pairs before and after line changeover are directly derived from the event segment of "line changeover start - line changeover end," and are used for subsequent estimation of the line changeover cost matrix. The identification of the line changeover cost matrix is ​​a mature practice, and in this invention, it is only necessary to explain that: attribute differences and attribute interactions are used as independent variables, and line changeover duration is used as the dependent variable. Least squares with non-negative constraints and weighted abnormal samples are used for identification, and shared priors are introduced at the equipment level to improve the stability of sparse workstations. Since the initial state has been guaranteed by structural consistency checks, the extracted line changeover samples have high reliability, avoiding the propagation of time deviations caused by missed or duplicate reporting.

[0051] The effectiveness of this step is reflected in three aspects. First, state accuracy: The combined constraints of the marker update formula and the place invariant formula ensure that the values ​​of work-in-process and queues are consistent with the flow, eliminating the arbitrariness of "resetting based on experience". Second, data availability: The initial state that has passed the consistency check can be directly used as the starting point for assimilation and prediction, reducing subsequent parameter drift; the filtered line change segments provide high signal-to-noise ratio samples for cost identification. Third, traceability: Each partial replay and repair is bound to a specific event segment, forming an auditable trajectory, which facilitates quality accountability and process review.

[0052] Example: Select a production line including cutting, sewing, ironing, and final inspection. Construct a process digital twin, defining the cutting exit, sewing entrance buffer, sewing station resources, ironing entrance buffer, and final inspection station as warehouses, and arrival, start, completion, changeover start, and changeover end as transitions. Collect barcode entry, work reporting, equipment start / stop, and cutting signals within one shift, and generate an event stream after unified timing. Play back events from the most recent watermark to the current time, triggering them one by one according to the marker update formula. After the first playback, perform conservation checks on the three sets of invariants, finding a deviation of 2 in the weighted sum of the sewing buffer and ironing entrance. Searching local events reveals duplicate entries of the same batch at the ironing entrance, which are identified as duplicate events, deleted, and replayed, with the deviation returning to zero. Thus, the initial state is obtained: 8 sewing entrance queues, 4 ironing entrance queues, 2 idle sewing stations, and the rest occupied or changing lines. Subsequently, 120 corrected "line change start - line change end" segments were extracted and organized into three-dimensional combinations of color, fabric, and size. Samples with abnormal durations were given low weights to complete cost identification. The identification results showed that the interaction items where color and fabric changed simultaneously were significant, indicating that this combination switch on this production line requires more preparation and verification. The initial state and cost results were then used by subsequent modules: the assimilation module updated the processing time distribution starting from this state, and the scheduling module used the cost matrix to constrain release and line change direction selection.

[0053] Hierarchical online assimilation of event flow is performed to update processing time distribution and line change cost matrix. A topology summary is generated based on work-in-process flow graph. Predicted arrival flow and capacity carrying capacity distribution are constructed and the coupling matrix is ​​solved by regularized optimal transmission. Koopman operator is identified to form counterfactual generator.

[0054] This invention views the event flow as a continuous observation of the process digital twin, and hierarchical online assimilation is used to calibrate the processing time distribution and changeover cost matrix in real time. Observations are derived from the processing duration of "start-to-finish" and the changeover duration of "changeover start-to-changeover end," with features including product attributes, equipment, and workstation condition characteristics. A recursive update method is employed.

[0055] ,

[0056] ,

[0057] ,

[0058] in, For a moment The parameter vector contains the estimated coefficients of the processing time distribution and the line change cost matrix; This is the actual measured duration; Based on The prediction duration of features; This is a first-order sensitivity matrix; For parameter covariance; To observe the noise covariance; The matrix is ​​an identity matrix. To suppress the impact of outlier observations, robust weights are introduced for outlier samples, and a shared prior is set at the equipment layer to ensure the stability of sparse workstations.

[0059] The work-in-process flow diagram uses processes as nodes and marked flows as directed edges, with edge weights equal to the number of times the process passes through the window or the amount of work-in-process. To characterize structural changes, a topology summary is calculated and compared with the previous window to obtain a stability measure of the bottleneck loop and merging structure. ,in, and This provides a topological summary of adjacent windows. This represents the bottleneck distance between the two. This value is used to trigger retraction and path rerouting in subsequent control operations to ensure structural consistency.

[0060] Predicted arrival flow describes future attributes—the distribution of arrivals on the time grid; capacity carrying capacity distribution describes bottlenecks—the processing capacity on the time grid. Both are balanced through regularization to achieve optimal transport balancing.

[0061] ,

[0062] in, This is the coupling matrix; The cost matrix is ​​a combination of attribute distance and normalized line-changing cost. The regularization coefficient is used. For entropy; To predict arrival flow; Distribution of production capacity; It is an all-1 vector. This solution ensures that the arrival side and the capacity side are aligned at the distribution level, providing a marginal load baseline for subsequent work-in-process quota and dual price calculations.

[0063] The counterfactual generator uses the Koopman operator for fast evaluation. First, it maps the state vector to an observable function, constructing features containing attribute pairs related to workpiece position, queue length, equipment state, and before / after line changeover. Then, it identifies counterfactual data through extended dynamic mode decomposition.

[0064] ,

[0065] ,

[0066] ,

[0067] in, For the observable function mapping of the state; For a moment The state; and For empirical moments; For the Koopman operator; Ridge coefficient; The number of samples; For generalized inverse. Use Short-term advancements can provide rapid incremental assessments of throughput, work-in-process, delays, and line change costs for micro-actions such as "batch release, batch rearrangement, process route switching, and line change direction selection." The top-ranked candidates then enter short-window discrete event simulation refinement to generate highly reliable counterfactual results.

[0068] The effects of the above-mentioned link are reflected in the following aspects: First, the parameters continuously converge with observation, and the processing time distribution and line change cost matrix remain consistent with the actual situation; second, the topology summary provides structural layer monitoring signals to promptly detect the deepening of bottleneck loops and abnormal merging; third, regularized optimal transmission achieves demand-capacity alignment at the distribution layer, laying the foundation for the smooth evolution of work-in-process quota allocation and dual prices; fourth, the Koopman operator enables micro-action evaluation to have millisecond-level response, providing computable priors for rolling optimization.

[0069] Example: This step is run on a production line including cutting, sewing, ironing, and final inspection. After collecting an 8-hour continuous event flow, hierarchical online assimilation is initiated. The processing time distribution of the sewing station converges to the new shift level within 1 hour, and the weight of the interaction term "simultaneous color and fabric change" in the changeover cost matrix is ​​increased. A work-in-process flow graph is constructed and a topology summary is generated. Compared to the previous window, the bottleneck distance increases, pointing to a deeper loop of "sewing buffer - ironing entry". A predicted arrival flow is generated based on sales rhythm and work-in-process status. The capacity carrying capacity distribution is obtained by combining the equipment calendar. The coupling matrix is ​​obtained through regularized optimal transmission. The results show that dark-colored items are concentrated in the ironing capacity in the second half of the window. After identifying the Koopman operator, the micro-action of "releasing dark-colored batches in advance and swapping them with light-colored batches" is quickly evaluated. The predicted peak of work-in-process decreases and the increase in changeover cost is acceptable. The conclusion remains consistent after entering the short window simulation and is used as the input for the next cycle of release and rearrangement. Through this process, the monitoring interface can simultaneously display parameter updates, structural signals, and distribution alignment results, while the scheduling end can use counterfactual assessments to support release sequencing and path selection, forming a closed loop from observation to decision-making.

[0070] Preferably, the hierarchical online assimilation updates parameters at the equipment, workstation, product, and batch levels, and applies robust weighting to anomaly observations in the event flow to suppress the offset of the processing time distribution and changeover cost matrix.

[0071] The goal of hierarchical online assimilation is to calibrate the processing time distribution and changeover cost matrix in real time as the process digital twin continuously receives event streams, ensuring that parameters simultaneously reflect differences in equipment and workstation capabilities, process differences in product attributes, and short-term fluctuations introduced by batches. To this end, each type of duration parameter is represented as the sum of the global baseline and four layers of biases, forming an interpretable and transferable structure. The core decomposition is as follows:

[0072] ,

[0073] in, Indicates time The parameter vector, which includes the estimated coefficients of the processing time distribution and the line change cost matrix; For global baseline; For device layer bias, index Identification equipment; For workstation layer bias, index Identify workstations; For product layer bias, index Identify combinations of product attributes; For batch layer bias, index Batch identification. All four biases are subject to shrinkage constraints, automatically regressing to zero when evidence is insufficient, ensuring robustness in small sample scenarios. Online assimilation is updated recursively at the granularity of single observations. For each pair of "start and finish" or "start and end of line change" events, the observation duration and attribute pairs before and after the line change are constructed as features. The predicted duration and residuals are calculated using the current parameters, and then updated with robust weights. The core recursion is as follows:

[0074] ,

[0075] in, This is the actual measured duration. For the reason The prediction time obtained from the features based on the attributes before and after the route change. For assimilation gain, These are robust weights. Robust weights are used to suppress the impact of outliers and take the form of adaptive thresholds:

[0076] ,

[0077] in, This is a median absolute deviation scale based on a sliding window. Gain Determined by sensitivity and uncertainty, it contains an allocation matrix for the four layers of bias, distributing the residuals according to their contribution to the equipment layer, workstation layer, product layer, and batch layer. The updating of covariance and the setting of the shrinkage coefficient are common practices in this field and are omitted here. The core is to ensure that the high-variance layer receives stronger shrinkage constraints.

[0078] The processing time distribution employs a logarithmic linear link to adapt to a positively skewed distribution, and the line-change cost matrix is ​​parameterized using attribute differences and attribute interactions as independent variables. The observed attribute pairs before and after line changes are uniformly derived from the state and color attribute vectors of the process digital twin, ensuring consistency between the assimilation criteria and subsequent scheduling. Anomaly observation and identification utilize two types of signals: one from equipment and workstation self-inspection flags, such as extreme durations caused by short-term downtime; and the other from event segments marked as low-confidence after structural consistency verification. Both types of signals act together on robust weights, minimizing data loss and reducing their impact on parameters.

[0079] At the implementation level, the equipment layer and workstation layer share prior knowledge to reflect the transferability of the same model of equipment or adjacent workstations. The product layer is characterized by combinations of color, fabric, and size, while the batch layer reflects short-term disturbances in personnel, materials, and the environment. Online assimilation is performed recursively according to the event time sequence, with parameter updates completed approximately every few seconds, forming a lightweight loop consistent with the rhythm of the event flow. After parameter updates, they are immediately fed back to the process digital twin for use in prediction and counterfactual assessment.

[0080] The aforementioned layering and robustness strategy delivers three types of benefits. First, it resists drift: abnormal reporting, temporary shutdowns, and a small number of missed reports no longer skew the overall parameters, and residuals are limited to a controllable range within a single update. Second, it enables rapid convergence: the batch layer quickly absorbs short-term changes, the product and workstation layers complete major adjustments within dozens of observations, and the equipment layer maintains slow and stable drift correction, exhibiting an overall "fast-medium-slow" timescale decomposition. Third, it allows for transferability: when a new workstation is launched or a new product is introduced for the first time, the layered structure allows it to inherit the historical knowledge of the equipment and product, requiring only a small number of batch layer observations to achieve usable accuracy, significantly reducing the cost of cold starts.

[0081] Example: This step is run on a production line including cutting, sewing, ironing, and final inspection. Layered online assimilation is initiated after collecting an 8-hour continuous event stream. Initially, the measured duration of sewing stations is significantly higher than the historical baseline, and the residuals are quickly absorbed into the batch-level bias, avoiding misinterpreting short-term fluctuations as equipment capability degradation. In the second hour, maintenance of a certain piece of equipment resulted in two extremely long observations. Robust weighting compressed the weights of the two observations to close to 0.3, and the equipment-level bias only underwent a minor correction, while the station-level and product-level biases remained relatively stable. In the fourth hour, a new color and fabric combination entered production. The product-level bias reached a stable estimate after approximately 20 observations and, together with the thread change segment, supported the incremental update of the thread change cost matrix. In the sixth hour, a shift change caused a short-term decrease in sewing time, which the batch-level bias absorbed within 30 minutes and then gradually returned to normal. At the end of the entire cycle, the logarithmic domain variance of the processing time distribution in the two key processes of sewing and ironing decreased by approximately 20% and 15%, respectively, and the confidence interval of the color and fabric interaction term in the changeover cost matrix converged significantly. Real-time parameter write-back enabled the prediction module to evaluate release and rearrangement based on the latest distribution, thereby reducing the number of times high-cost changeover directions were selected by the scheduling end, and the monitoring end visualized the evolution trajectory of the biases at each layer, facilitating dual-line review of the process and equipment.

[0082] Preferably, the topology summary is obtained by persistent cohomology calculation of the product flow graph and topology changes are measured by the bottleneck distance between adjacent time windows, which is used to trigger withdrawals and path rerouting.

[0083] In the digital twin monitoring of multiple processes in the garment industry, the work-in-process flow diagram uses processes as nodes and the directional relationships between work-in-process passing and waiting as edges. The edge weights are obtained by normalizing the number of passes or the average waiting time within a time window. This diagram reflects the actual flow direction and accumulation pattern of materials between processes. To obtain structural quantities that are directly related to scheduling and comparable across windows, this invention uses persistent cohomology as a tool to map the work-in-process flow diagram into a topological structure summary. This summary is used to identify persistent parallel merging and ring-shaped congestion patterns, and the topological distance between adjacent time windows characterizes the intensity of structural changes.

[0084] The calculation path for the topology summary is as follows: A filter sequence with increasing thresholds is generated from the work-in-process flow graph; birth and death trajectories of homology features are constructed to obtain the persistence spectrum. To match the scheduling objective, this invention focuses on the one-dimensional homology features corresponding to loop structures; the greater the persistence, the higher the risk of work-in-process cyclically accumulating along multiple pathways. After matching the topology summaries of adjacent windows, the bottleneck distance is used to measure the intensity of structural changes, serving as a criterion for triggering withdrawals and path rerouting.

[0085] The core quantities are defined as follows:

[0086] ,

[0087] ,

[0088] in, Homophony characteristics Durability, and These are the birth and death levels, respectively; and A topological summary (persistent graph) of adjacent time windows; This is the bottleneck distance; The optimal matching between the two graphs. Triggering logic writing:

[0089] ,

[0090] in, The threshold for structural change. The persistence threshold is defined by the quantiles of the historical distribution. The above expression is only used to define the trigger quantity; the specific threshold calibration and numerical solution adopt methods commonly used in this field.

[0091] In practical implementation, the time window length and step interval are consistent with the monitoring refresh cycle. To avoid the influence of directionality on cohomology calculation, the process flow diagram is undirected or bidirectionally weighted symmetric when calculating the loop structure, maintaining sensitivity to large-scale loops. The topology summary contains three types of information: feature count, total persistence, and the set of contributing edges for high-persistence paths. The set of contributing edges is extracted from the edge weight-feature relationship using a back-substitution algorithm, used to locate the process connections that contribute the most to the loop structure, providing operable objects for subsequent withdrawal and path rerouting.

[0092] The mapping of topology quantities to control follows the principle of "isolation first, then rerouting." When the trigger signal is true, the batches of work not yet started on high-persistence loops are first filtered out according to the set of contributing edges to form a withdrawal list. The withdrawal operation does not change the continuity of already started operations. Subsequently, in the set of feasible process paths, the topology impact of each candidate path is quantified using counterfactual evaluation, prioritizing alternative paths that reduce bottleneck distance without increasing line-changing costs or delay risks. At the same time, the intensity of topology change is used as a structural item in the scheduling cost and as a reference for adjusting work-in-process quotas. In the short term, the work-in-process quotas on high-persistence loops are tightened to reduce the probability of further exacerbating the loop.

[0093] The effectiveness of the above mechanism is reflected in three aspects. First, the structure is observable: the topology summary quantifies structural phenomena such as "whether a ring congestion occurs" and "whether merging becomes heavier" into comparable scalars and edge sets, facilitating cross-shift and cross-day comparisons. Second, the triggering is interpretable: bottleneck distance and maximum persistence correspond to specific pathways and batches, providing clear indications and evidence for withdrawals and route rerouting. Third, the coupling is closed-loop: topology triggering forms a closed loop with work-in-process quotas, dual prices, and counterfactual assessments, avoiding short-sighted adjustments based solely on local queue length signals.

[0094] Example: A topology summary module is deployed on a production line including cutting, sewing, ironing, and final inspection. The window length is set to 30 minutes and the step size to 5 minutes. In the window from the 3rd hour to the 3rd hour and 30th minute, the topology summary is calculated, and the loop corresponding to the maximum durability spans "sewing buffer - ironing entrance - ironing buffer - sewing entrance". The bottleneck distance compared with the previous window is 0.12, which exceeds the threshold of 0.08, triggering a true signal. The contributing edge set is located to the two edges "sewing buffer → ironing entrance" and "ironing buffer → sewing entrance". Based on this, the system generates a withdrawal list containing 12 unstarted batches located on the subsequent paths of the above two edges. For each withdrawn batch, a counterfactual evaluation compares two alternatives in the set of feasible process paths: one is to delay the entry to the next time grid, and the other is to execute another sequence with the same fabric first. The evaluation showed that the second option resulted in a more significant reduction in the expected bottleneck distance without increasing the cost of line switching. Based on this, the system generated a path rerouting instruction and simultaneously tightened the work-in-process quota for the paths containing the two aforementioned edges to 0.9 of the original value. In the next window, the bottleneck distance decreased to 0.07, the maximum persistence decreased, the loop structure eased, and the withdrawal strategy was discontinued, retaining only the path rerouting and a slight tightening of the work-in-process quota. Throughout the process, the topology summary, withdrawal list, path rerouting, and changes to the work-in-process quota were all recorded as auditable evidence for use in process review and equipment co-optimization.

[0095] Preferably, the cost matrix of the regularized optimal transmission is composed of a weighted average of the product attribute difference metric and the normalized value of the line-changing cost matrix, and the coupling matrix is ​​solved by Sinkhorn iteration.

[0096] This invention aligns predicted arrival flows with capacity carrying capacity distribution at the distribution layer using regularized optimal transport. The source end is a discrete grid of attributes and time, and the target end is a discrete grid of bottlenecks and time. The coupling matrix describes the allocation intensity of each type of arrival at each bottleneck time period. The key is to construct a cost matrix that fits the process physics, so that the allocation simultaneously follows the constraints of attribute compatibility and line change cost. Attribute compatibility is measured by attribute embedding vectors, and line change constraints are given by the line change cost matrix, which, combined with the attribute pairs before and after line change in the digital twin, forms a normalized line change cost. The attribute embedding vectors are consistent with the process genome coding mentioned above, used to characterize the impact of color, fabric, size, and accessory combinations on processing and switching.

[0097] The cost matrix is ​​constructed as follows. Let the source element be denoted as... Let be the arrival time of a raster cell at a given time for a certain combination of attributes; denoted as the target cell. Let be the available capacity of a grid at a given time for a particular bottleneck; let the attribute embedding vector be . The bottleneck preference vector is The bottleneck preference vector is obtained by regression of historical assignments and equipment characteristics. The attribute difference is measured using Euclidean distance.

[0098] ,

[0099] The normalized lane-changing cost is derived from the lane-changing cost matrix and the attribute pairs before and after the lane change. Let... Given the combination of attributes to be processed before the target unit, the line-changing cost function is: Normalize by taking the maximum value:

[0100] ,

[0101] in, This is the upper bound or a high-quantile normalized constant for the historical line-changing cost. The weighted cost is obtained by combining these factors:

[0102] ,

[0103] in, and As weight, satisfying Larger Emphasizing attribute compatibility, larger Emphasis is placed on suppressing line switching losses. After construction, a regularized optimal transmission solution is performed:

[0104] ,

[0105] in, Let be the coupling matrix. To predict the arrival flow, For capacity carrying capacity distribution, The regularization coefficient is . For entropy, The vector is composed of all 1s. The Sinkhorn iteration is used for efficient solution. Let the kernel matrix be:

[0106] ,

[0107] Then there is a scaling solution. The iterative update is as follows:

[0108] ,

[0109] ,

[0110] Where 0 represents element-wise division. and The scaling vector is used. Iteration continues until the marginal constraints meet the accuracy requirements. To ensure numerical stability, the kernel matrix and scaling vector employ conventional methods such as logarithmic field or threshold truncation, which will not be elaborated upon further.

[0111] The application significance of this design is reflected in three aspects. First, physical consistency. The attribute difference term prioritizes matching bottleneck periods with homogeneous attributes, and the normalized switching cost term allows allocation to avoid periods and directions with high switching costs, reducing unnecessary switching at the distribution level. Second, cross-window comparability. Regularization and normalization stabilize the cost scale, and the coupling matrix can be directly used for expected load and smoothing strategies in different time windows. Third, scheduling availability. The row and column margins of the coupling matrix directly give the expected load of each bottleneck in the future time period, which can be used as input for work-in-process quotas and dual prices, and serve as a prior allocation field when evaluating candidate actions.

[0112] Example: On a production line including cutting, sewing, ironing, and final inspection, with a time step of 10 minutes, the arrival flow is predicted to provide the arrival volume of color and fabric combinations in the next six time grids. Capacity carrying capacity distribution provides the capacity of the two bottlenecks, sewing and ironing, in their corresponding time grids. Attribute embedding vectors are trained using historical data, ensuring that the vector distance between denim fabric and dark colors at the sewing bottleneck is small, while the vector distance with the ironing bottleneck is large, reflecting the process sensitivity of the two bottlenecks. Attribute pairs before and after line change are obtained from the digital twin, yielding the preceding attribute combination for each bottleneck time grid. The normalized line change cost is calculated based on the line change cost matrix. Weights are set. and satisfy Based on the recent frequency of line replacement, select the larger one. To mitigate the costs associated with the impending large number of cuts, a cost matrix was constructed, followed by the calculation of the kernel matrix and approximately 50 Sinkhorn iterations to obtain the coupling matrix. Results showed that dark denim was more frequently assigned to sewing bottlenecks already in the dark sequence in the first half of the window, while light-colored woven fabrics were matched with ironing capabilities in the second half, with row and column margins consistent with the input distribution. The coupling matrix was aggregated into the bottleneck expected load, serving as the baseline for work-in-process quota allocation and a smoothing reference for dual price updates. Subsequently, in candidate action evaluation, the system accordingly reduced the number of cross-color thread change direction selections, favored same-color-first schemes in the release sequence, and decreased the cycle persistence in the topology summary, indicating that cyclic congestion was alleviated.

[0113] Preferably, the identification of the Koopman operator is based on the observable function mapping of the state vector, which includes a polynomial expansion of the product position, queue length, equipment state and attribute pairs before and after line change, and the stability of the counterfactual generator is guaranteed by the spectral radius constraint.

[0114] This invention elevates the discrete event evolution of process digital twins to an observable function space, utilizing linear operators to approximate nonlinear dynamics, thereby evaluating the incremental impact of micro-actions such as batch release, batch rearrangement, process path switching, and line change direction selection at the millisecond level. The state vector consists of the work-in-process position, the length of the entry queue for each process, equipment availability and shutdown flags, and attribute pairs before and after line change. The attribute pairs before and after line change record the previous and next attribute combinations, enabling subsequent cost and state response linkage.

[0115] The observable function mapping consists of polynomial extensions of the aforementioned state variables, including first-order terms, second-order interaction terms, and interaction terms with attribute pairs before and after line switching. Components with different dimensions are standardized to ensure numerical stability. The mapping dimension is set according to the principle of "sufficient to express the dominant coupling relationship between the queue and work-in-process, without causing excessive dimensionality explosion," generally using second- or third-order dimensions to cover common concurrency and merging effects.

[0116] The identification of the Koopman operator employs an empirical matrix form of extended dynamic mode decomposition:

[0117] ,

[0118] ,

[0119] ,

[0120] in, For observable function mapping, For a moment The state vector, For the sample size, For ridge parameters, It is the identity matrix. This is the generalized inverse. To suppress the impact of anomalous observations, samples marked as low confidence by equipment self-checks or structural verifications are given low weights when constructing the empirical matrix, without changing the framework, only adjusting the sample contribution. Identification is performed on a sliding window to adapt to changes in work groups, materials, and environment.

[0121] To ensure the numerical stability of the counterfactual generator during short-term propagation, a spectral radius constraint is introduced. First, the spectral radius is calculated:

[0122] ,

[0123] like Exceeding the preset upper limit (Based on the prediction steps and refresh cycle settings), perform shrinkage projection:

[0124] ,

[0125] in, To allow for a small margin, ensuring that the contraction remains strictly within the stable region. This process does not change the characteristic direction, only scaling the amplitude proportionally to avoid divergence during short-term rolling. Subsequently, a linear propagation approximation is used to approximate the short-term effects of the micro-motions.

[0126] ,

[0127] in, To predict the number of steps, the throughput, peak work-in-process inventory, delay, and changeover cost increments are calculated based on the predicted work-in-process position, queue length, and attribute pairs before and after the changeover, combined with the assimilated processing time distribution and changeover cost matrix. These increments are used as the first-level screening of candidate actions. The few actions ranked at the top then enter the short-window discrete event simulation refinement.

[0128] The application focus of this design is not on building a "perfect model," but on providing a stable, interpretable, and fast approximation consistent with digital twins: observable function mapping clarifies which physical quantities are at play; spectral radius constraints ensure controllability within the rolling prediction window; and linear advancement allows the relative merits of hundreds or thousands of candidate actions to be given within the refresh cycle, buying time for subsequent ranking and work-in-process quota adjustments.

[0129] Example: On a production line including cutting, sewing, ironing, and final inspection, the refresh cycle is set to 5 minutes, and the training window is set to 90 minutes. The state vector includes the work-in-process position and queue length for the four processes, equipment availability and shutdown flags, and attribute pairs before and after line changeover. The observable function mapping uses a second-order polynomial and introduces interaction terms with the attribute pairs before and after line changeover, with a dimension of approximately several hundred. An empirical matrix is ​​constructed using a sliding window, and the Koopman operator is identified, with parameters automatically adjusted based on the verification error. The identified spectral radius is slightly higher than the upper bound during individual shift handovers, but recovers to the stable region after shrinking projection. Two types of actions, "releasing dark batches in advance and swapping them with light batches" and "retaining the current order but delaying entry," are quickly evaluated. Linear progression provides an incremental ranking of the work-in-process peak and line changeover cost, showing that the former is more beneficial for reducing the circumferential congestion between sewing and ironing. Subsequently, short-window simulation is performed in a digital twin, and the results are consistent with the ranking of the quick evaluation. The release sequence generated based on this sorting reduces the bottleneck distance of the topology summary in subsequent windows, resulting in a more balanced queue distribution and shorter recovery time after equipment downtime. Throughout the process, the updates of the Koopman operator, the spectral radius and shrinkage coefficient, and the residual distribution of the first-level evaluation are all recorded, facilitating the review of abnormal periods.

[0130] Within the rolling prediction window, the dual price vector is calculated based on the assimilated processing time distribution, the line change cost matrix, and the coupling matrix. The upper limit of the work-in-process capacity is quantified into the work-in-process quota. The counterfactual generator is called to evaluate the incremental cost of batch release and rearrangement and to generate a release sequence by prioritizing the best results.

[0131] This invention, within a fixed-length rolling prediction window, uses the assimilated processing time distribution and line-changing cost matrix as the parameter basis for service and switching, and the coupling matrix obtained from regularized optimal transmission as the distribution basis for demand and capacity, to establish a dual price vector to characterize the congestion intensity of each bottleneck at each time grid. Let the bottleneck identifier be... The time grid is The predicted work-in-process curve is The maximum capacity is The dual price vector is updated using subgradient form:

[0132] ,

[0133] in, For dual prices, Step size, It is a non-negative projection. To suppress short-term jitter, it is combined with the coupling matrix. Obtain the expected load of each bottleneck Based on this, It provides a light smoothing effect in time and space, allowing the dual price to remain continuous as demand and capacity change slowly.

[0134] The upper limit of work-in-process capacity is discretized into work-in-process quotas, which are executable constraints used for release and rearrangement. Let the quota be... It is determined by both capacity and expected load:

[0135] ,

[0136] in, For safety factors, if the actions involved in releasing or rescheduling cause the quota of the corresponding path to exceed the limit in any bottleneck time grid, then the action cannot be executed in this cycle. Quotas and dual prices form a soft and hard constraint, the former limiting the number of work-in-process that can be advanced, and the latter quantifying the marginal congestion cost of advancement.

[0137] The merits of candidate actions are measured by incremental metrics provided by the counterfactual generator. For any candidate action... The counterfact generator returns changes in work-in-process inventory, changes in line changeover costs, and changes in delays, denoted as follows: , , The overall incremental cost is defined as:

[0138] ,

[0139] in, and Using as the weight, a unified dimension is established between switching costs and delay losses. If the structural penalty has already been calculated in the previous section, it is then used as... Add the above formula, symbol For structural weights, Incremental quantification for topology changes. The sorting phase, provided quotas are feasible, is based on... By selecting the best from the smallest to the largest, we obtain the release sequence and the necessary rearrangement sequence for this cycle.

[0140] This step contributes to monitoring and scheduling in three ways. First, congestion becomes quantifiable. The dual price vector transforms "where there is congestion and to what extent" into summable marginal costs, facilitating comparisons across bottlenecks and time periods. Second, constraints become enforceable. Work-in-process quotas transform abstract capacity limits into consumable and returnable amounts, directly constraining the feasibility of release and rearrangement. Third, evaluation becomes closed-loop. The counterfactual generator provides incremental responses consistent with the process digital twin, and together with dual prices and work-in-process quotas, establishes the "evaluation-sequencing-execution" chain on the same physical caliber.

[0141] Example: On a production line including cutting, sewing, ironing, and final inspection, a rolling prediction window is set to 60 minutes with a step size of 5 minutes. Service capacity curves for each bottleneck at each time grid are generated from the assimilated processing time distribution, and the expected load for each bottleneck is obtained by aggregation using a coupling matrix. After calculating the dual price vector, the work-in-process quota is obtained according to the above rules. A candidate action set is constructed, including partial swaps and path switching of batches awaiting release and batches not yet started. For each candidate action, a counterfactual generator is invoked to obtain changes in work-in-process, line change cost, and delay. Incremental costs are calculated using the dual price vector, line change cost weight, and delay weight. After filtering out quota infeasibility items, the sequence is sorted. The generated release sequence prioritizes paths with similar attributes and lower dual prices, and the rearranged sequence is used to eliminate local peaks. Observations in the next window show that the peak work-in-process value between sewing and ironing decreases, and the bottleneck distance in the topology summary falls back, indicating that the congestion situation has eased. The dual price and work-in-process quota are updated with the rolling window, and the release strategy remains stable without excessively frequent switching.

[0142] Preferably, the dual price vector is updated using the sub-gradient rule and spatially smoothed using a graph Laplace constructed based on the coupling matrix. Temporal smoothing is performed on the dual price vector of adjacent periods when the capacity carrying capacity distribution changes little.

[0143] In digital twin monitoring of multiple processes in garment manufacturing, the dual price vector is used to measure the congestion intensity of each bottleneck at each time grid, serving as the marginal cost weight for release and rearrangement. Let the bottleneck index be... The time grid is The predicted work-in-process inventory is The maximum capacity is The dual price is First, update the baseline dual price in the form of subgradients, as expressed by:

[0144] ,

[0145] in, Step size, It is a non-negative projection. This update directly maps the magnitude of "work in progress exceeding limits" to congestion intensity, ensuring interpretability and feasibility.

[0146] To avoid unnecessary and drastic spatial differences in dual prices, it is necessary to use a coupling matrix to induce similar structures between bottlenecks and perform spatial smoothing. Let the coupling matrix be... ,element Representation of attributes and time grid cells At the bottleneck Time Grid The intensity of the allocation. Define the bottleneck similarity weight within the same time grid:

[0147] ,

[0148] Thus, the Laplace matrix is ​​obtained. ,in Let be a diagonal matrix, where the diagonal elements are the sums of the rows.

[0149] Subgradient results Using the baseline, perform first-order graph regularization smoothing:

[0150] ,

[0151] in, Let be the dual price vector of all bottlenecks within the same grid at the same time, and λ be the smoothing coefficient. The closed-form optimal solution of this objective satisfies The solution can be obtained quickly using conjugate gradients. Spatial smoothing makes the dual prices of bottlenecks with highly overlapping demand sources tend to be consistent, reducing local fluctuations caused by statistical noise.

[0152] When capacity carrying capacity varies little between adjacent cycles, further time smoothing can be performed to suppress cross-cycle oscillations. Let the expected bottleneck load be... The bearing variation between adjacent periods is measured using the Wasserstein distance:

[0153] ,

[0154] when Execution of exponential time smoothing:

[0155] ,

[0156] in, For the change threshold, This is the time smoothing coefficient. This gating ensures smoothing of dual prices when the load pattern is stable and maintains a fast response during load abrupt changes.

[0157] The implementation process is as follows: In each rolling prediction window, first calculate the assimilated processing time distribution and capacity limit. and After completing the subgradient update, we obtain Subsequently, similarity weights and Laplace's equations are constructed using the coupling matrix, and the graph regularization objective is solved to obtain... Finally, time smoothing is performed based on the load change threshold to obtain... and put It is handed over to the counterfactual assessment and release sorting module for use.

[0158] The above mechanism brings three benefits. First, stability: the two-level smoothing of space and time significantly reduces the high-frequency fluctuations of dual prices, avoiding frequent reversals of the release strategy in adjacent windows. Second, consistency: it establishes price linkages between bottlenecks with similar demand sources, prompting the release of work-in-process from a globally optimal perspective. Third, interpretability: each level of smoothing has clear data support, facilitating the tracing of the source of dual price changes during audits and reviews.

[0159] Example: On a production line with two bottlenecks—sewing and ironing—the time grid is 5 minutes, and the rolling prediction window is 60 minutes. The results are calculated based on the assimilated processing time distribution. The capacity limit is derived from the shift calendar and equipment availability. After updating by sub-gradient, it is stitched into the 6th time grid. The overlap of demand sources for the two bottlenecks in this grid is statistically analyzed using the coupling matrix, resulting in a similarity weight close to 1. After graph Laplace smoothing, the price difference between the two converges to half. Subsequently, the Wasserstein distance between adjacent cycles is calculated to be 0.02, which is below the threshold of 0.05, indicating smoothed execution time. We set the value to 0.4. The final dual price enters the release sorting, and the system tends to release batches with similar grid attributes that simultaneously alleviate congestion in both bottlenecks at that time. In the next window, we observe a decrease in the peak value of work-in-process, a reduction in unnecessary line switching, and a decrease in the bottleneck distance in the topology summary, proving that the price signal and scheduling actions form a stable closed loop.

[0160] Preferably, when the upper limit of work-in-process capacity is quantified as work-in-process quota, the work-in-process quota is allocated according to bottlenecks and time periods, atomic locking is implemented for process paths that cross multiple bottlenecks, and the corresponding work-in-process quota is released according to the path after the operation is completed.

[0161] The principle of work-in-process quotas is to transform capacity constraints from static upper limits into discrete, consumable, and returnable quotas, enabling release and reordering to be executed simultaneously in both time and path dimensions. A set of quotas is allocated to each bottleneck and time period, and the quota for each job at each bottleneck is locked in one go, avoiding mid-journey congestion caused by "first come, first served" scenarios. The quota is released back to the ledger immediately after the job passes the bottleneck, thus maintaining a stable cycle of work-in-process.

[0162] Quota allocation is based on capacity limits and expected load. Let the bottleneck index be... The time period is The maximum capacity is Expected load is The safety factor is Work-in-process quota is .

[0163] ,

[0164] in, Obtained by aggregation of coupling matrices, it indicates which bottleneck should be allocated during that time period. Expected workload; This is used to leave a buffer to absorb random disturbances. Atomic locking requires checking and locking the required amount once before the job enters the path. Let the job identifier be... The set of bottlenecks involved in its process path is The task is at a bottleneck The set of occupied time periods is The current amount of credit used is The amount applied for this time is The feasibility assessment is as follows:

[0165] ,

[0166] ,

[0167] If all conditions are met, then atomic locking is performed, and the quota is simultaneously transferred from all... The available balance is deducted from the locked balance; if either condition is not met, the job will not be issued in this cycle to prevent inconsistent occupancy across bottlenecks.

[0168] Credit limit deductions and releases follow ledger updates. Let the locking operation be denoted as... The release operation is recorded as . (Locked) When the job is at a bottleneck time period When completed: (Release) To prevent long-term occupation, the ledger is equipped with a timeout recovery and abnormal rollback mechanism. Locked amounts that do not trigger a completion event after the timeout are recovered to the available balance and recorded in the evidence log for easy traceability.

[0169] The implementation process includes three points. First, the credit limit ledger maintains available balance, locked balance, and historical release volume using bottlenecks and time periods as keys, all updated with timestamps to ensure consistency with the event flow. Second, path consistency checks are performed in a two-phase commit before issuance: a pre-check of all constraints followed by a one-time commit of the locks to ensure atomicity. Third, release rules are bound to completion and outbound events, derived from event replay in the process digital twin, requiring no human intervention.

[0170] The design delivers three key benefits. First, it prevents mid-journey congestion. Atomic locking ensures that "once it enters, it leaves," eliminating cross-bottom deadlocks caused by partial locking. Second, it smooths work-in-process inventory. Quotas are allocated based on bottlenecks and time periods, controlling peak work-in-process inventory levels and reducing queue fluctuations. Third, it facilitates auditing. Each locking and releasing operation has a timestamp and path anchor, allowing for direct review of release strategies and anomaly handling.

[0171] Example: In a production line with two bottlenecks—sewing and ironing—the time interval is 5 minutes. Based on the assimilated processing time distribution and the equipment calendar, calculations are performed. and Based on the aggregation of coupling matrices, the following is obtained: and Pick calculate A certain assignment The process path sequentially involves sewing and ironing. It is estimated that one unit of credit will be used each in the 3rd and 4th sewing time slots, and one unit of credit will be used in the 5th ironing time slot, forming... , , After the system checks that all three balances meet feasibility requirements, it executes an atomic lock, deducting the amount from all three locations simultaneously. The sewing operation is immediately checked (sewing, ...) upon completion and departure from the station. ) and (sewing, Release credit limit upon completion of ironing (ironing, Release quota. If ironing timeout occurs due to equipment failure, the timeout recovery rule will lock the quota and return the available balance, and mark the operation as abnormal, adding it to the scheduling avoidance list for the next cycle. During this cycle, a decrease in the peak value of the sewing entry queue was observed, no new waiting queues appeared at the ironing entry, and the ring persistence in the topology summary decreased, indicating that atomic locking and path-based release effectively suppressed work-in-process backflow and local circulation.

[0172] Preferably, the incremental cost is weighted by the product of the dual price and the change in work-in-process, the incremental cost of line switching, the incremental cost of delay, and the structural penalty term based on the topology summary. A two-level evaluation process is adopted, in which the first level is a fast evaluation based on the Koopman operator, and the second level is a short-window discrete event simulation refinement evaluation.

[0173] This invention quantifies the impact of candidate actions into a single scalar to support comparable ranking within a rolling prediction window. Candidate actions refer to batch release, batch reordering, process path switching, and line change direction selection. The design philosophy is to aggregate the costs of congestion, switching, and delivery into a single metric, while penalizing "structural deterioration" to avoid the accumulation of circular congestion caused by local optima.

[0174] The core incremental cost is defined as:

[0175] ,

[0176] in, Number the candidate actions; bottleneck In the time grid The dual price represents the marginal congestion cost per unit of work-in-process at that location; For action The resulting change in work-in-process inventory; For action The resulting increase in line switching cost is calculated based on the line switching cost matrix and attribute pairs before and after the line switching. For action For incremental delivery delays, the aggregation is based on the difference between the batch delivery date and the expected completion time; For action The quantification of topological degradation is derived from topological structure summarization; The weights are used to map costs of different dimensions to a unified scale. The product of dual price and work-in-process change reflects the marginal impact of "where to push work-in-process"; the line change and delay terms reflect the direct costs of "switching and delivery"; the structural penalty term inhibits actions that lead to an increase in the distance to high-endurance loops or bottlenecks.

[0177] The two-level evaluation process is as follows. The first level is a rapid evaluation, using the Koopman operator to linearly advance the state in the short term, obtaining an approximate value of the observable function of the state vector after several steps. This value is then mapped to changes in work-in-process inventory, changes in line change costs, and delays, forming... The rapid evaluation covers all candidates and is completed within the refresh cycle, generating a reliable relative ranking. The second stage is a refined evaluation, where a small number of actions ranked high in the first stage are simulated using a short-window discrete event model on a colored-delay Petri net. Service time and switching time are derived from the assimilated processing time distribution and switching cost matrix, resulting in high-fidelity simulations. , , And based on the counterfactual path, the topology summary of the work-in-process flow graph is recalculated to obtain If the deviation between the refined result and the rapid result exceeds a threshold, the refined result will be used to override the rapid value.

[0178] The methods for obtaining each increment are as follows: Work-in-process changes are obtained from the state difference before and after rapid advancement or refining simulations; the changeover cost increment is based on the slicing sequence triggered by the action and the attribute pairs before and after the changeover, with each attribute pair being substituted into the changeover cost matrix and summed; the delay increment is based on the batch delivery date set, with non-negative difference aggregation of the portion exceeding the expected completion time; structural penalties are extracted from the topology summary, defined by the change in bottleneck distance or maximum durability between adjacent windows.

[0179] ,

[0180] in, For action Summary of future window topology This is a summary of the future window topology of the baseline scheme. For bottleneck distance, Let this be the window step size. Using the non-negative part ensures that penalties are only applied to "worse" structural changes. Weights , , The switching costs, delivery losses, and structural risk preferences of enterprises can be calibrated on a weekly rolling basis.

[0181] To ensure the sorting is feasible, all candidates must pass a feasibility check under the constraints of work-in-process quotas and process paths before pricing; those that are not feasible are directly eliminated. After sorting, the release sequence and necessary rearrangement sequences are output; if multiple... If they are close, they will be broken up in the order of "lower structural penalty first, lower line switching cost first".

[0182] The benefits are reflected in three aspects. First, comparability: different types of actions are compared under a unified standard, avoiding the bias of single indicators such as "only looking at queue length" or "only looking at the number of switches". Second, low latency: the two-level evaluation places most of the computation in the fast layer, while the refinement layer only covers the top few, meeting the time limit within the rolling window. Third, robustness: the structural penalty term suppresses potential circular congestion accumulation, preventing short-term gains from causing long-term deterioration.

[0183] Example: In a production line including sewing and ironing, the rolling forecast window is 60 minutes with a step size of 5 minutes. A candidate action set is constructed, including three categories: early release of a dark-colored batch, swapping with a light-colored batch, and maintaining the order but delaying entry. The first-level evaluation uses the Koopman operator to advance to the next 6 steps, obtaining approximate increments for the three action types: early release reduces the peak value of work-in-process, slightly increases the cost of changing lines, and reduces delays; swapping reduces the peak value of work-in-process even more, but significantly increases the cost of changing lines; delayed entry slightly reduces the peak value of work-in-process, and increases delays. Combining the current dual price vector and weights, The order is "early release", "delayed entry", and "swap". Selecting the first two items for refined simulation yields the following results. , , The high fidelity value was calculated. Early release reduces bottleneck distance, with a structural penalty of 0; delayed entry has no structural deterioration, with a penalty of 0. (Refined) Maintaining the same sorting order, the system generates a release sequence accordingly: releasing dark-colored batches first, then maintaining the original order for other batches; a decrease in the peak value of work-in-process in the next window's sewing and ironing sections was observed, the bottleneck distance in the topology summary decreased, and no additional thread change direction switching occurred. The two-level evaluation log records the differences and acceptance criteria between rapid and refined processes, facilitating auditing and review.

[0184] The process path is locked and issued based on the work-in-process quota, reversible fine-tuning is implemented based on the deviation between the expected state and the execution state, and withdrawal and path rerouting are triggered based on the topology summary.

[0185] This invention places capacity constraints at the executable layer: the upper limit of work-in-process capacity is discretized into work-in-process quotas, which are stored in the ledger using "bottleneck-time period" as the key. Before entering the process path, each job performs a consistency check and atomically locks all bottlenecks and time period quotas along its path, ensuring that "once it enters, it completes." Let the job identifier be... The bottleneck set is The task is at a bottleneck The set of occupied time periods is The application amount is The current amount of credit used is Work-in-process quota is The feasibility and atomic locking conditions are as follows: When satisfied, in all Synchronously deduct and generate lock records; after the job completes the corresponding bottleneck, the quota is released segment by segment according to the path, and the ledger and event flow are aligned by timestamps to form an auditable trajectory.

[0186] To suppress bias accumulation during execution, reversible fine-tuning is introduced. The desired state is given by a counterfactual fast assessment over a short-run step, and the execution state is derived from event stream replay. Let time be... The desired state is The execution status is The weight matrix is (Used to unify the dimensions of different state components), the deviation metric is:

[0187] ,

[0188] when When the threshold is exceeded, a set of fine-tuning actions is triggered (partial swapping of batches not yet started, release delay, batch fine-tuning). Candidate actions are then considered. The advantages and disadvantages are determined by the incremental cost defined above. The assessment, along with constraints on quota feasibility and path consistency, determines the optimal action: Atomic locking is feasible and does not change the continuity of already started work. Fine-tuning is first verified in the digital twin in the form of shadow work orders, and then converted into formal issuance; if the verification fails, it is immediately withdrawn without changing the ledger balance.

[0189] At the structural level, a topology summary triggering mechanism is used to control rollback and path rerouting. The topological distance between adjacent windows is denoted as... Maximum durability is .when or At this time, the system generates a withdrawal list for batches that have not yet started work and are located on high-persistence loops, refunds the locked amount in full according to the path, selects an alternative path from the set of feasible process paths based on the principle of minimum incremental cost, and issues a path rerouting instruction. For work that has already started, only subsequent local adjustments are performed on the path rerouting, without interrupting the current processing.

[0190] The overall benefits of this design are reflected in the following aspects: First, quota-path consistency ensures that release and rearrangement naturally meet capacity constraints, avoiding "first-come, first-served" bottlenecks. Second, deviation closure ensures that the expected-actual deviation during the execution period is corrected reversibly within the current cycle, preventing error propagation. Third, structural protection transforms structural risks such as "deepening circular congestion" into explicit withdrawal and rerouting actions, reducing the probability of oscillations and deadlocks. Fourth, strong auditability ensures that locking, releasing, withdrawal, and rerouting are all bound to specific event segments, facilitating traceability.

[0191] Example: On a production line including sewing and ironing, the time granularity is 5 minutes, and the rolling forecast window is 60 minutes. Work-in-process quotas are calculated based on capacity limits and expected loads and recorded in the ledger. A certain dark-colored batch... The plan involves deducting quotas from three positions and issuing work orders simultaneously after the quota check meets the atomic locking conditions during the 3rd and 4th sewing time periods and the 5th ironing time period. During the 4th time period, the expected-to-actual deviation (ete_tet) increases due to a short-term downtime during ironing. The system generates two fine-tuning candidates: swapping the unstarted light-colored batches or delaying the current dark-colored batches by one time period. Based on the incremental cost and quota feasibility assessment, the delay option has a smaller incremental cost and does not require additional thread-changing costs. The system officially issues the work order after verification with a shadow work order. Subsequently, the topology summary shows that the bottleneck distance between the sewing buffer and the ironing entrance has increased beyond the threshold, triggering structural protection. The unstarted light-colored batches located upstream of this ring are partially withdrawn, the corresponding quotas are returned, and a same-color-first alternative path is selected. At the end of this period, the peak work-in-process inventory between sewing and ironing decreases, the number of thread-changing direction switches decreases, the topology distance falls back, and all locking and releasing records and action decisions are written to the evidence log for subsequent review.

[0192] Preferably, reversible fine-tuning includes batch swapping and inbound delay operations for batches that have not yet started. The triggering conditions for withdrawal and route rerouting are that the structural indicators of the topology summary exceed a threshold. Route rerouting selects an alternative route from the set of feasible process routes based on the principle of minimizing incremental cost.

[0193] The principle of reversible fine-tuning is to apply minimal disturbance to unstarted batches without interrupting already started work, thereby realigning the work-in-process distribution with the desired trajectory while adhering to work-in-process quotas and process path constraints. The desired trajectory is derived from counterfactual rapid assessment, and the execution status is derived from event stream replay. Weighted deviation is used to characterize execution deviation, serving as the fine-tuning trigger.

[0194] ,

[0195] in, For a moment The execution state vector, Let be the desired state vector. Let be the weight matrix for each state component. If If the threshold is exceeded, a candidate action set for the unstarted batch is generated at the corresponding bottleneck entry point, including batch swapping and inbound delay actions. Each candidate action is verified in the digital twin using a shadow work order; only those that pass verification are formally issued. Actions that fail verification are withdrawn, and the ledger balance and work-in-process quota remain unchanged. The quality of candidate actions is determined by the incremental cost defined above. A unified metric is used, and the best choice is made based on work-in-process quotas and the feasibility of atomic locking. Let the set of candidate actions be denoted as... A feasible solution is The feasibility of in-process quotas and atomic locking is checked, and the feasibility check follows the aforementioned determination of quota balance, so it will not be repeated. The swap operation exchanges the queuing positions of two batches within the same bottleneck and time period; the inbound delay operation postpones the inbound time of a single batch by a certain number of grids, and neither of these changes the process continuity of the batches that have already started.

[0196] Undoing and route rerouting are triggered by exceeding the threshold of the topology summary's structural indicators. Let the topology summaries of the current window and the previous window be... and The bottleneck distance is Maximum durability is The trigger criterion is...

[0197] ,

[0198] in, and The threshold is used. Upon triggering, firstly, based on the contribution edge set, the batches that have not yet started are located on the high-persistence ring, a withdrawal list is generated, and their locked amounts are returned according to the path. Then, an alternative path is selected for each withdrawn batch from the set of feasible process paths. The set of feasible paths is denoted as [missing information]. The path selection is Through a feasibility check of product quotas and atomic locking, among which, For batch Use path The incremental cost at that time. The alternative path is only implemented on batches that have not yet started; for batches that have already started, only the subsequent unstarted sections are partially rerouted without interrupting the current processing.

[0199] The key aspects of this mechanism include three points. First, fine-tuning precedes withdrawal: when deviations are caused by short-term disturbances, batch swapping and inbound delays are used for rapid reset, avoiding frequent withdrawals at the structural level. Second, the entire process is reversible: shadow work orders are withdrawn if verification fails, without permanently affecting work-in-process quotas and ledger balances; officially issued actions only apply to batches that have not yet started. Third, path selection is executable: the generation and selection of alternative paths are integrated with the digital twin process. Figure 1 This satisfies both the sequential relationship and the work-in-process quota and atom locking constraints, avoiding the "first-occupied, then-deficient" situation after the rerouting.

[0200] The application's effectiveness is reflected in four aspects. First, deviation suppression: reversible fine-tuning eliminates the deviation between expectation and execution within a single cycle, reducing cross-cycle accumulation. Second, congestion relief: when structural indicators rise, withdrawals and rerouting shift the load from the loop channel to an alternative channel, which, combined with work-in-process quotas and dual prices, can sustainably reduce loop congestion. Third, stable release: the order of fine-tuning followed by withdrawal reduces the high-frequency jitter of the release strategy, making the release sequence change more stable. Fourth, auditability: each swap, delay, withdrawal, and rerouting action is accompanied by a timestamp, work-in-process quota change record, and incremental cost details, facilitating accountability and strategy review.

[0201] Example: On a production line that includes sewing and ironing, the time grid is 5 minutes, and the rolling prediction window is 60 minutes. At the 12th grid, a short-term downtime during ironing causes a deviation between expected and actual results. Increase. The system generates two reversible fine-tuning candidates at the ironing inlet: swap the 2nd and 3rd unstarted batches in the queue, or postpone the 2nd batch by one grid. A counterfactual quick evaluation is invoked to obtain the results for both. The delayed solution has a smaller incremental cost and passes quota and atomic lock checks. After verification with a shadow work order, the system officially issues the work order. In the next window, the bottleneck distance in the topology summary exceeds a threshold, triggering structure protection. A withdrawal list is generated for unstarted batches located on the "sewing buffer—ironing entrance—ironing buffer—sewing entrance" ring. The locked quota is returned according to the path, and the work order is then added to the set of feasible process paths based on… Select the same alternative path as the current fabric. After execution, the next window observes a decrease in the peak work-in-process inventory, a reduction in the number of line change direction switching times, and a decrease in bottleneck distance. The shadow verification results of all actions, the official issuance time, and the deduction and return of work-in-process quotas are all written to the evidence log for easy review later.

[0202] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A digital twin monitoring method for multiple processes in garment manufacturing, characterized in that, Includes the following steps: A process digital twin represented by a colored time-delay Petri net is established. Production signals are mapped to event streams according to a unified event dictionary. The initial state is determined by event playback and the changeover cost matrix is ​​estimated accordingly. Hierarchical online assimilation of event flow is performed to update processing time distribution and line change cost matrix. A topology summary is generated based on work-in-process flow graph. Predicted arrival flow and capacity carrying capacity distribution are constructed and the coupling matrix is ​​solved by regularized optimal transmission. Koopman operator is identified to form counterfactual generator. The topology summary is obtained by persistent cohomology calculation of the product flow graph and topology change is measured by the bottleneck distance between adjacent time windows, which is used to trigger withdrawal and path rerouting. The cost matrix of regularized optimal transmission is composed of a weighted average of the product attribute difference metric and the normalized value of the line-changing cost matrix, and the coupling matrix is ​​solved by Sinkhorn iteration. The identification of the Koopman operator is based on the observable function mapping of the state vector, which includes a polynomial expansion of the product position, queue length, equipment state and attribute pairs before and after the changeover, and the stability of the counterfactual generator is guaranteed by the spectral radius constraint. Within the rolling prediction window, the dual price vector is calculated based on the assimilated processing time distribution, the line change cost matrix, and the coupling matrix. The upper limit of the work-in-process capacity is quantified into the work-in-process quota. The counterfactual generator is called to evaluate the incremental cost of batch release and rearrangement and to generate a release sequence by prioritizing the best results. The process path is locked and issued based on the work-in-process quota, reversible fine-tuning is implemented based on the deviation between the expected state and the execution state, and withdrawal and path rerouting are triggered based on the topology summary.

2. The method according to claim 1, characterized in that, The determination of the initial state adopts the consistency check of event playback and place invariant to ensure that the process digital twin and the event flow maintain the conservation consistency in the number of tags and the direction of flow.

3. The method according to claim 1, characterized in that, Layered online assimilation updates parameters at the equipment, workstation, product, and batch levels, and applies robust weighting to anomaly observations in the event flow to suppress the offset of the processing time distribution and changeover cost matrix.

4. The method according to claim 1, characterized in that, The dual price vector is updated using the subgradient rule and spatially smoothed using a graph Laplace constructed based on the coupling matrix. Temporal smoothing is performed on the dual price vector of adjacent periods when the capacity carrying capacity distribution changes little.

5. The method according to claim 1, characterized in that, When the upper limit of work-in-process capacity is quantified into work-in-process quota, the work-in-process quota is allocated according to bottlenecks and time periods. Atomic locking is implemented for process paths that cross multiple bottlenecks, and the corresponding work-in-process quota is released according to the path after the operation is completed.

6. The method according to claim 1, characterized in that, The incremental cost is weighted by the product of the dual price and the change in work-in-process, the incremental cost of line switching, the incremental cost of delay, and the structural penalty term based on the topology summary. It adopts a two-level evaluation process, in which the first level is a fast evaluation based on the Koopman operator, and the second level is a short-window discrete event simulation refinement evaluation.

7. The method according to claim 1, characterized in that, Reversible fine-tuning includes batch swapping and entry delay operations for batches that have not yet started. The triggering conditions for withdrawal and route rerouting are that the structural indicators of the topology summary exceed the threshold. Route rerouting selects alternative routes from the set of feasible process routes based on the principle of minimizing incremental cost.

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