A real-time monitoring method for a thermal paper coating production line

Abstract

This invention discloses a real-time monitoring method for thermal paper coating production lines, relating to the field of product monitoring technology. The method includes: constructing a fused data volume; forming a dynamic topological directed graph; inputting the singular spectrum width into a nonlinear mapping function to obtain the nonlinear saturated response coefficient and dynamic critical collapse threshold corresponding to each spatial point; obtaining the final abnormal propagation heatmap of the coating state; and locating the root cause of the abnormality based on the risk classification results. This invention introduces a multifractal detrended fluctuation analysis method to explore the fluctuation patterns of the wet film thickness sequence at different time scales. It quantifies the complexity of local fluctuations in the coating through singular spectrum characteristics, generates nonlinear saturated response coefficients and dynamic collapse thresholds, and captures latent signs of local instability that cannot be identified by conventional statistical indicators. This allows for risk prediction before the appearance of obvious defects such as sagging and stringing, effectively advancing the quality early warning window.

Description

Technical Field

[0001] This invention relates to the field of product monitoring technology, specifically a real-time monitoring method for a thermal paper coating production line. Background Technology

[0002] The coating production of thermal paper is a continuous, high-speed process. The uniformity of coating and the degree of drying directly determine the color development, coating adhesion, and appearance quality of the finished product. Real-time process monitoring of the production line is a core element in ensuring product consistency and reducing raw material waste. As coating speeds continue to increase and product categories iterate more rapidly, the shortcomings of existing monitoring technologies in anomaly prediction and process adaptability are becoming increasingly apparent.

[0003] Current conventional coating production line monitoring mostly adopts a single-parameter independent threshold alarm mode. Process data such as coating die pressure, wet film thickness, temperature and humidity of each drying zone, and traction tension are isolated from each other and do not combine the material transfer relationship between processes and the control coupling logic for correlation analysis. Therefore, it cannot reflect the propagation and evolution of abnormalities along the direction of substrate travel. Usually, by the time the downstream inspection station identifies obvious defects such as sagging, color difference, and uneven thickness, a long number of defective products have already been produced, and the early warning has a significant lag.

[0004] Meanwhile, existing monitoring models generally use fixed thresholds and static analysis logic. When quality anomalies occur, most companies in the industry rely on the experience of operators to investigate the root cause station by station. Moreover, the coating production line has a long process link and complex parameter coupling relationships, and the propagation path of anomalies is hidden. Manual investigation is not only inefficient, but also prone to root cause location errors. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a real-time monitoring method for thermal paper coating production lines, comprising the following specific steps: S1. After aligning the timestamps of the sensor signals acquired by the multi-sensor modules, a two-dimensional process variable matrix is ​​formed. The production progress information and progress factor of the day are added to the side of the two-dimensional process variable matrix to form a fused data body. S2. Based on the material flow direction and energy coupling path of the production line, a dynamic topological directed graph is formed by assigning initial weights and determining the effective feedforward gain based on the progress factor. S3. Based on the row vector of wet film cross section thickness distribution in the fused data volume, the local deviation distribution matrix of wet film thickness is formed by difference calculation. Combined with the hot air temperature and wind speed alignment values ​​applied to spatial discrete points by each drying zone, it is converted into a drying intensity feedback distribution matrix. By introducing multifractal detrending fluctuation analysis, the singular spectrum width is input into the nonlinear mapping function to obtain the nonlinear saturation response coefficient and dynamic critical collapse threshold corresponding to each spatial point. S4. Based on the distribution matrix of local deviation of wet film thickness as the initial value of the coating state activation field and the distribution matrix of drying intensity feedback as the initial value of the coating state suppression field, anisotropic diffusion is performed. After each diffusion is completed, collapse detection is performed by using the linear saturation response coefficient and the dynamic critical collapse threshold. After iterative loop, the final coating state abnormal propagation heat map is obtained. S5. Based on the absolute values ​​of the activation values ​​of all spatial points in the heat map of abnormal propagation of coating state, a non-negative sequence is formed. After being converted into a probability distribution, the risk classification is completed by calculating the non-extensive entropy, and the root cause of the anomaly is located based on the risk classification results.

[0006] Preferably, step S1 aligns the sensor signals acquired by the multiple sensor modules according to a unified timestamp. In specific implementations, these sensor signals include the transverse distribution sequence of pressure at the coating die slit, the pulse sequence of the substrate's running linear velocity, the alignment vector group of hot air temperature and wind speed in each drying zone, the wet film cross-sectional thickness distribution matrix acquired by the online wet film thickness scanner, the time sequence of the colorimetric tristimulus values ​​acquired by the dry film colorimeter, and the time sequence of the effective torque current of each traction roller motor driver. The time reference is unified to the frame pulse generated by the oven inlet trigger sensor. In the thermal paper coating production line, the substrate runs continuously. If each sensor uses its own independent sampling clock, the wet film thickness and drying temperature acquired at the same time actually correspond to different positions on the substrate. Using the oven inlet frame pulse as a unified time reference is equivalent to converting the sampling coordinate system from laboratory time to the longitudinal position of the substrate, and extracting a time cross-section according to the sampling time. The continuous variables distributed along the width direction at each time section are expanded into row vectors according to spatial discrete points. This includes the thickness values ​​in the wet film cross-section thickness distribution arranged in a row along the spatial discrete points, and the measured values ​​of the hot air temperature in each drying zone along the width position arranged into corresponding row vectors according to the same spatial discrete points. Furthermore, the row vectors of adjacent time sections are stacked in chronological order to form a two-dimensional process variable matrix. As can be seen from the above, the matrix constructed in this application stacks the cross-sections, making the time dimension the vertical axis of the matrix, which is equivalent to solidifying the process memory of the production line into a searchable structure. Based on the manufacturing execution system, the daily production progress information is read, including the number of rewinding rolls completed that day, the total length of the current order to be coated in meters, and the product code. Based on the equipment control system, the real-time status words of the overall equipment are read, including the binary bit image of the dryer fan health, winding tension control mode, and calender roller vibration over-limit flag. The ratio of the remaining length of the set to be coated in meters to the running time is mapped to the progress factor. This application further discloses the mapping method, including that when the theoretical completion time corresponding to the remaining length of meters is shorter than the preset proportion of the remaining available time of the current shift, the tension factor increases from zero to one by linear interpolation; otherwise, it remains at zero. The specific value of the increase is controlled by a linear relationship. Each binary bit value of the overall real-time status word of the progress factor is appended to the side of the two-dimensional process variable matrix of each time segment to form a three-dimensional tensor block carrying the time dimension, spatial dimension, equipment health dimension and production rhythm dimension. The three-dimensional tensor blocks of all time segments are arranged in time sequence to form a fused data volume.

[0007] Preferably, S2 abstracts the functional stations into graphical nodes based on the material flow direction and energy coupling path of the thermal paper coating production line, including the first node corresponding to the coating die head coating area, the second node corresponding to the first suspension drying area, the third node corresponding to the second impact drying area, the fourth node corresponding to the third tempering drying area, the fifth node corresponding to the online wet film detection station, the sixth node corresponding to the dry film color detection station, the seventh node corresponding to the calendering roller group, and the eighth node corresponding to the winding traction station. Between adjacent nodes with material transfer relationships, a forward material transfer edge is established with the direction consistent with the substrate travel direction. Between the downstream detection station and the upstream adjustment station, a reverse control coupling edge is established with the direction pointing from the detection station back to the adjustment station. This includes the direction from the dry film color detection station to the hot air actuators in each drying zone, and the direction from the winding traction station to the material supply pressure setting of the coating die head.

[0008] Preferably, S2 assigns an initial weight to each directed edge and, by reading the overall real-time status word of the device in the fused data body, applies a decay to the initial weight of the relevant edges according to the preset device status. It should be noted that the initial weight is calibrated through a step response test under steady-state conditions on the production line. The calibration method is as follows: a step disturbance is applied to the upstream node, the response delay and amplitude gain of the downstream node are recorded, and the amplitude gain is normalized and multiplied inversely by the delay to obtain the initial transmission strength of that edge. After the initial transmission strength is established, when the status word indicates that the output of a heating tube group in a drying zone is affected... When the preset limit is reached, the weights of all forward material transfer edges and reverse control coupling edges starting from the corresponding node of the drying zone are multiplied by an attenuation coefficient less than one. The attenuation coefficient is quantified by the damping during the propagation process. The progress factor in the fused data body is read, and the weights of all reverse control coupling edges are multiplied by one minus the product of the progress tension factor to complete the final assignment of each edge weight. The weights of each edge are recalculated for each time segment based on the current equipment status word and progress factor. The adjacency matrix and edge weight vector at the current time are output to form a dynamic topological directed graph.

[0009] Preferably, step S3 extracts the wet film cross-sectional thickness distribution row vector from the two-dimensional process variable matrix at the current moment based on the fused data volume. This row vector stores the measured wet film thickness value at each spatial discrete point along the width direction. Based on each spatial discrete point of the wet film cross-sectional thickness distribution row vector, the wet film thickness value of the corresponding spatial discrete point under the same product in multiple stable production periods in the past is extracted, and the median value is used as the reference value of the wet film thickness at the spatial discrete point. Because the thermal paper coating liquid is a thixotropic non-Newtonian fluid, its coating thickness always has a small amplitude pulsation at the microscopic level. Therefore, this application... The median, rather than the arithmetic mean, is used as the benchmark because occasional thickness spikes may occur during product switching, material receiving, or short-term shutdown recovery. The average value will be skewed by such spikes, while the median is not sensitive to such outliers and can more stably represent the target thickness at that point under normal process conditions. The wet film thickness value of each spatial discrete point in the row vector at the current moment is subtracted from the corresponding wet film thickness benchmark value to obtain the wet film thickness deviation at the point. When there is a point with a negative wet film thickness deviation, the differences of all spatial discrete points are arranged in the original spatial order to form a distribution matrix of local deviation of wet film thickness. Based on each spatial discrete point, the corresponding values ​​of hot air temperature and wind speed applied by each drying zone to the spatial discrete point are extracted. Based on the evaporation intensity mapping, which refers to the mapping relationship established by measuring the solvent evaporation mass per unit time under different temperature and wind speed combinations, the equivalent evaporation driving force value is obtained. The equivalent evaporation driving force of all drying zones to the spatial discrete point is summed and the difference is calculated with the evaporation driving force benchmark value of the spatial discrete point under the historical stable production period to obtain the drying intensity feedback deviation of the spatial discrete point. The drying intensity feedback deviation of all points is arranged in spatial order to form a drying intensity feedback distribution matrix. Thus, temperature and wind speed are combined into an equivalent evaporation driving force, which is equivalent to unifying the complex multivariate drying control into a single physical quantity that can be directly coupled with the wet film thickness deviation. Its positive or negative sign indicates whether the drying system is enhancing or weakening the solvent evaporation at that point, thus forming a suppression field that antagonizes the activation field.

[0010] Preferably, S3 extracts the wet film thickness sequence of each spatial discrete point in the width direction from the fused data volume within a preset time window, the time window length covering several times the product of the production line running speed and the characteristic time of the drying cycle. By performing multifractal detrending fluctuation analysis on the wet film thickness sequence, including subtracting the mean of the entire sequence from each value of the wet film thickness sequence, and then accumulating the values ​​one by one starting from the first value, a cumulative deviation sequence reflecting the degree of cumulative deviation is obtained. In this application, because the original fluctuation of the coating wet film thickness is an oscillation around the benchmark value, its direct autocorrelation structure is difficult to distinguish between true long memory and short-range artifacts. Therefore, after being converted into a cumulative deviation sequence, the persistent deviation in the original sequence is manifested as a long-range trend in the cumulative sequence, while random perturbations are averaged out, making multi-scale scaling behavior easier to detect. The cumulative deviation sequence is divided into equal parts according to a time scale that increases in multiples from a preset minimum scale until it does not exceed a preset proportion of the total length of the sequence. Based on each time scale, the cumulative deviation sequence is divided into several non-overlapping segments of equal length. If there are any remaining segments at the end that are not enough to form a complete segment, the sequence is divided in reverse order from the end of the sequence to ensure that all data points are utilized. Since the film thickness is affected not only by random disturbances, but also by the macroscopic trends of gradual changes in vehicle speed, room temperature drift, and batch-to-batch viscosity of coating liquid, the cumulative deviation data of each equal-length segment is fitted into a second-order polynomial using the least squares method. The root mean square value of the fitted residual is calculated and used as the local fluctuation magnitude of the equal-length segment. By fitting the internal trend of the segment with a second-order polynomial and removing the residual, these macroscopic slow-drift components can be filtered out, while retaining the fluctuation information generated by microscopic dynamics such as coating leveling, solvent evaporation, and wind impact. Based on the selected fluctuation weighting order, the local fluctuation magnitudes of all equal-length segments at the same time scale are respectively mapped to the power of the fluctuation weighting order. After averaging, the average value is taken as the reciprocal of the corresponding fluctuation weighting order to obtain the fluctuation function value corresponding to the fluctuation weighting order at the time scale. Based on the set of points depicting the change of the corresponding fluctuation function value with the time scale in a double logarithmic coordinate system for each fluctuation weighting order, a weighted least squares straight line fitting is used, and the slope of the obtained straight line is used as the generalized scaling exponent corresponding to the fluctuation weighting order. Thus, this application constructs a generalized scaling exponent for the power law relationship of the wet film thickness fluctuation with the observation scale at the corresponding order. If the exponent changes significantly with the order, the sequence has multifractal characteristics; if it remains almost unchanged, it is monofractal, meaning that the fluctuation structure is simple. In particular, by offline analysis of the wet film thickness sequences of historical normal batches and batches containing known defects, the correlation between the generalized scaling exponent and the severity of defects at each order is calculated, and the orders with significant correlation are retained as a preset set.

[0011] Preferably, step S2 derives the multifractal singular spectrum from the generalized scaling exponent corresponding to each fluctuation weighting order through Legendre transformation. The singular spectrum width is input into a nonlinear mapping function. By establishing the correspondence between the singular spectrum width at each point within the historical normal range and the allowable upper limit of the wet film thickness fluctuation at the corresponding spatial discrete point, a nonlinear saturated response coefficient for the spatial discrete point is output. The spectral asymmetry of the multifractal singular spectrum is added to the absolute value of the deviation at the corresponding spatial discrete point in the current drying intensity feedback distribution matrix after smoothing and amplitude limiting to obtain the dynamic critical collapse threshold for the spatial discrete point. When a point is already in a high-load correction state of the drying system, it means that the current wet film deviation has approached or exceeded the normal adjustment range, with little remaining correction margin. At this time, even a small additional disturbance may cause the deviation to exceed the coating's tolerable limit, triggering sudden defects such as sagging and stringing. Therefore, this application superimposes the absolute value of the drying intensity feedback deviation onto the threshold, quantifying the currently consumed control resources as a reduction in the additional disturbance tolerance capability of that point, making the collapse judgment and production line real-time... The control saturation is directly related. For each wave weighting order, an intermediate quantity called the quality index is calculated. Its value is the wave weighting order multiplied by the corresponding generalized scaling exponent minus one. Then, for adjacent wave weighting orders, the ratio of the difference in the quality index to the difference in the wave weighting order is calculated as the singularity index. Using the singularity index and the corresponding wave weighting order, the singular spectrum value is obtained, which is the wave weighting order multiplied by the singular index minus the quality index. All points obtained are plotted with the singular index as the x-axis and the singular spectrum value as the y-axis. Connecting these points yields the singular spectrum curve, and the width of the singular spectrum curve is the difference between the maximum and minimum values ​​among all singular indices, known as the singular spectrum width. The spectral asymmetry is a measure of the difference between the descent rates of the left and right halves of the curve. It should be noted that the singular spectrum width corresponds to the multi-scale complexity of coating uniformity. A wide width indicates that multiple fluctuation modes, such as slow drift and sudden jumps, coexist at that point, which is a statistical sign of local instability in the coating. The spectral asymmetry, on the other hand, indicates the dominance of the fluctuation modes.

[0012] Preferably, in step S4, the distribution matrix of local deviation of wet film thickness is used as the activation value of the coating state activation field, and the distribution matrix of drying intensity feedback is used as the activation value of the coating state suppression field. Each spatial discrete point corresponds to a node in the dynamic topological directed graph. In each time iteration step, an anisotropic diffusion operation is performed, including: based on the coating state activation field, each node diffuses to the downstream neighbor node connected along the forward material transfer edge. The diffusion flux is equal to the edge weight multiplied by the difference between the activation value of this node and the activation value of the neighbor node. If the difference is positive, the activation value flows out from this node; if it is negative, it flows in from the neighbor node. This updates the activation value of each node. The principle is that in the process of the substrate, the area of ​​local thickness of wet film will migrate downstream longitudinally due to the flow parallelism of the coating itself and the airflow shearing effect of the hot air in the subsequent oven. During the migration, the excess coating will gradually spread or redistribute. The edge weight controls the amount of migration and is modulated by the equipment status and production rhythm, simulating the effectiveness of this longitudinal migration under different working conditions. Based on the coating state suppression field, each node is diffused in reverse to the upstream node connected along the reverse control coupling edge. The diffusion flux is equal to the weight of the reverse edge multiplied by the difference between the suppression value of this node and the suppression value of the upstream node, and the suppression value of each node is updated. After diffusion is complete, all nodes are traversed. When the activation value of any node exceeds the dynamic critical collapse threshold, the excess deviation of the activation value exceeding the dynamic critical collapse threshold is calculated. The excess deviation is distributed to downstream neighboring nodes according to the weight ratio of all forward material transmission edges of the corresponding node and superimposed on the activation value of the neighboring nodes. The detection is then re-executed for the neighboring nodes that receive the superimposed excess deviation. If their activation value exceeds their own dynamic critical collapse threshold, secondary collapse is triggered and the distribution and suppression of jumps are repeated until the activation values ​​of all nodes are lower than their respective dynamic critical collapse thresholds. After the collapse detection is completed, the activation values ​​of each node are extracted and arranged into a two-dimensional matrix according to the spatial discrete point order to form the abnormal propagation heat map of the coating state at the current moment.

[0013] Preferably, step S4 is based on taking the absolute values ​​of the activation values ​​of all discrete spatial points in the abnormal propagation heatmap of the coating state to form a non-negative sequence. After normalizing the non-negative sequence, it is transformed into a probability distribution. The non-extensive parameter is determined by maximizing the ratio of inter-class distance to intra-class variance of historical normal and abnormal working condition heatmap samples. The non-extensive parameter is raised to the power of each probability value in the probability distribution. All the obtained values ​​are summed to obtain a sum. The difference between one and the sum is divided by the non-extensive parameter minus one to obtain the non-extensive entropy value. Because the non-extensive entropy adjusts the sensitivity to extreme probabilities through the power scaling parameter, isolated bright paths can significantly increase the overall entropy value. Therefore, this application provides an early warning of sudden coating defects through non-extensive entropy. Based on the progress factor read from the fused data body at the current moment, it is compared with the non-extensive entropy value through the quantile threshold of normal fluctuation of non-extensive entropy under different progress factor intervals. The quantile threshold is constructed by offline self-sampling of high confidence upper bounds from historical data of the same type and speed segment. When the extensive entropy exceeds the quantile threshold corresponding to the current progress factor, the corresponding risk level is output, including slightly exceeding the corresponding attention level and significantly exceeding the corresponding intervention level.

[0014] Preferably, in step S4, based on the risk level, the node with the most cumulative collapses is selected as the end of the propagation chain from the collapsed nodes. The upstream adjacent nodes are traced backward hop by hop along the forward material transfer edge of the dynamic topology directed graph. By statistically analyzing the cumulative collapse count of each node and the average magnitude of the excess deviation at each collapse on the backtracking path, since the defect propagation direction of the thermal paper production line is consistent with the substrate running direction, the collapse signal is always transmitted from upstream to downstream step by step. The node with the highest cumulative collapse count and the suppression feedback lags behind the growth of the activation value is marked as a suspected initial instability source. The stored production status information of the day is retrieved. If the key node position on the backtracking path coincides with the product switching timestamp, the abnormality is obtained as a batch difference of the coating liquid.

[0015] Beneficial effects This invention provides a real-time monitoring method for thermal paper coating production lines, which has the following beneficial effects: it introduces a multifractal detrended fluctuation analysis method to explore the fluctuation pattern of wet film thickness sequence at different time scales, quantifies the complexity of local fluctuations of coating through singular spectrum features, generates nonlinear saturated response coefficients and dynamic collapse thresholds, captures local instability latent signs that cannot be identified by conventional statistical indicators, completes risk prediction before the appearance of obvious defects such as sagging and stringing, and effectively moves the quality early warning window forward; The coating state activation field is constructed using the wet film thickness deviation, and the inhibition field is constructed using the drying intensity feedback. Combined with anisotropic diffusion and cascade collapse iteration, the propagation, suppression and amplification process of anomalies along the process link is simulated. Finally, a heat map of coating state anomaly propagation is generated, which can intuitively show the spatial distribution and evolution trend of anomalies, and help operators quickly grasp the spread range and impact of risks. By tracing back hop by hop along the topology of the abnormal propagation link and combining node collapse characteristics with production-related information to locate the initial instability source, it is possible to quickly distinguish between coating end, drying end, or material batch anomalies. This replaces the traditional manual segment-by-segment troubleshooting mode, shortens the time for fault location and process adjustment, and reduces the output of non-conforming products and downtime losses. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating a real-time monitoring method for a thermal paper coating production line according to the present invention. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] Please see Figure 1 This invention provides a real-time monitoring method for a thermal paper coating production line, comprising the following specific steps: S1. After aligning the timestamps of the sensor signals acquired by the multi-sensor modules, a two-dimensional process variable matrix is ​​formed. The production progress information and progress factor of the day are added to the side of the two-dimensional process variable matrix to form a fused data body. S2. Based on the material flow direction and energy coupling path of the production line, a dynamic topological directed graph is formed by assigning initial weights and determining the effective feedforward gain based on the progress factor. S3. Based on the row vector of wet film cross section thickness distribution in the fused data volume, the local deviation distribution matrix of wet film thickness is formed by difference calculation. Combined with the hot air temperature and wind speed alignment values ​​applied to spatial discrete points by each drying zone, it is converted into a drying intensity feedback distribution matrix. By introducing multifractal detrending fluctuation analysis, the singular spectrum width is input into the nonlinear mapping function to obtain the nonlinear saturation response coefficient and dynamic critical collapse threshold corresponding to each spatial point. S4. Based on the distribution matrix of local deviation of wet film thickness as the initial value of the coating state activation field and the distribution matrix of drying intensity feedback as the initial value of the coating state suppression field, anisotropic diffusion is performed. After each diffusion is completed, collapse detection is performed by using the linear saturation response coefficient and the dynamic critical collapse threshold. After iterative loop, the final coating state abnormal propagation heat map is obtained. S5. Based on the absolute values ​​of the activation values ​​of all spatial points in the heat map of abnormal propagation of coating state, a non-negative sequence is formed. After being converted into a probability distribution, the risk classification is completed by calculating the non-extensive entropy, and the root cause of the anomaly is located based on the risk classification results.

[0019] S1 aligns the sensor signals acquired by multiple sensor modules according to a unified timestamp. In specific implementation, these sensor signals include the transverse distribution sequence of pressure in the coating die slit, the pulse sequence of substrate running linear velocity, the alignment vector group of hot air temperature and wind speed in each drying zone, the wet film cross-sectional thickness distribution matrix acquired by the online wet film thickness scanner, the time sequence of colorimetric tristimulus values ​​acquired by the dry film colorimeter, and the time sequence of the effective torque current of each traction roller motor driver. The time reference is unified to the frame pulse generated by the oven inlet trigger sensor. In the thermal paper coating production line, the substrate runs continuously. If each sensor uses its own independent sampling clock, the wet film thickness and drying temperature acquired at the same time actually correspond to different positions on the substrate. Using the oven inlet frame pulse as a unified time reference is equivalent to converting the sampling coordinate system from laboratory time to the longitudinal position of the substrate, and capturing a time cross-section according to the sampling time. The continuous variables distributed along the width direction at each time section are expanded into row vectors according to spatial discrete points. This includes the thickness values ​​in the wet film cross-section thickness distribution arranged in a row along the spatial discrete points, and the measured values ​​of the hot air temperature in each drying zone along the width position arranged into corresponding row vectors according to the same spatial discrete points. Furthermore, the row vectors of adjacent time sections are stacked in chronological order to form a two-dimensional process variable matrix. As can be seen from the above, the matrix constructed in this application stacks the cross-sections, making the time dimension the vertical axis of the matrix, which is equivalent to solidifying the process memory of the production line into a searchable structure. Based on the manufacturing execution system, the daily production progress information is read, including the number of rewinding rolls completed that day, the total length of the current order to be coated in meters, and the product code. Based on the equipment control system, the real-time status words of the overall equipment are read, including the binary bit image of the dryer fan health, winding tension control mode, and calender roller vibration over-limit flag. The ratio of the remaining length of the set to be coated in meters to the running time is mapped to the progress factor. This application further discloses the mapping method, including that when the theoretical completion time corresponding to the remaining length of meters is shorter than the preset proportion of the remaining available time of the current shift, the tension factor increases from zero to one by linear interpolation; otherwise, it remains at zero. The specific value of the increase is controlled by a linear relationship. Each binary bit value of the overall real-time status word of the progress factor is appended to the side of the two-dimensional process variable matrix of each time segment to form a three-dimensional tensor block carrying the time dimension, spatial dimension, equipment health dimension and production rhythm dimension. The three-dimensional tensor blocks of all time segments are arranged in time sequence to form a fused data volume.

[0020] Based on the material flow direction and energy coupling path of the thermal paper coating production line, S2 abstracts the functional stations into graphical nodes, including the first node corresponding to the coating die head coating area, the second node corresponding to the first suspension drying area, the third node corresponding to the second impact drying area, the fourth node corresponding to the third tempering drying area, the fifth node corresponding to the online wet film detection station, the sixth node corresponding to the dry film color detection station, the seventh node corresponding to the calendering roller group, and the eighth node corresponding to the winding traction station. Between adjacent nodes with material transfer relationships, a forward material transfer edge is established with the direction consistent with the substrate travel direction. Between the downstream detection station and the upstream adjustment station, a reverse control coupling edge is established with the direction pointing from the detection station back to the adjustment station. This includes the direction from the dry film color detection station to the hot air actuators in each drying zone, and the direction from the winding traction station to the material supply pressure setting of the coating die head.

[0021] S2 assigns an initial weight to each directed edge and, by reading the overall real-time device status word in the fused data body, applies a decay to the initial weight of the relevant edges according to the preset device status. In this application, it should be noted that the initial weights are calibrated through step response tests under steady-state conditions of the production line. The calibration method is as follows: apply a step disturbance to the upstream node, record the response time delay and amplitude gain of the downstream node, normalize the amplitude gain and multiply it inversely with the time delay to obtain the initial transmission strength of the edge. After the initial transmission strength is established, when the status word indicates that the output of the heating tube group in a certain drying zone is limited to a preset level, the weights of all forward material transmission edges and reverse control coupling edges starting from the corresponding node of the drying zone are multiplied by an attenuation coefficient less than one. The attenuation coefficient is quantified by the damping during the propagation process. It reads the progress factor in the fused data body, multiplies the weights of all reverse control coupling edges by one minus the progress tension factor product, and completes the final assignment of each edge weight. It recalculates the edge weights of each edge based on the current device status word and progress factor at each time segment, and outputs the current adjacency matrix and edge weight vector, which together form a dynamic topological directed graph.

[0022] S3 extracts the wet film cross-sectional thickness distribution row vector from the two-dimensional process variable matrix at the current moment based on the fused data volume. This row vector stores the measured wet film thickness value at each spatial discrete point along the width direction. Based on each spatial discrete point of the wet film cross-sectional thickness distribution row vector, it extracts the wet film thickness value of the corresponding spatial discrete point under the same product in multiple stable production periods in the past, and uses the median value as the benchmark value of the wet film thickness at the spatial discrete point. Because the thermal paper coating liquid is a thixotropic non-Newtonian fluid, its coating thickness always has small fluctuations at the microscopic level. Therefore, this application uses the median value instead of the arithmetic mean as the benchmark because the production line will produce occasional thickness spikes when switching products, receiving materials, or recovering from a short shutdown. The average value will be skewed by such spikes, while the median value is not sensitive to such outliers and can more stably represent the target thickness of the point under normal process conditions. Subtract the corresponding wet film thickness reference value from the wet film thickness value of each spatial discrete point in the row vector at the current time to obtain the wet film thickness deviation at the point. When there is a point where the wet film thickness deviation is negative, arrange the differences of all spatial discrete points in the original spatial order to form a distribution matrix of local deviation of wet film thickness. Based on each spatial discrete point, the corresponding values ​​of hot air temperature and wind speed applied by each drying zone to the spatial discrete point are extracted. Based on the evaporation intensity mapping, which refers to the mapping relationship established by measuring the solvent evaporation mass per unit time under different combinations of temperature and wind speed, the equivalent evaporation driving force value is obtained. The equivalent evaporation driving force of all drying zones to the spatial discrete point is summed and the difference is calculated with the evaporation driving force benchmark value of the spatial discrete point under the historical stable production period to obtain the drying intensity feedback deviation of the spatial discrete point. The drying intensity feedback deviation of all points is arranged in spatial order to form a drying intensity feedback distribution matrix. Thus, this application combines temperature and wind speed into an equivalent evaporation driving force, which is equivalent to unifying the complex multivariate drying control into a single physical quantity that can be directly coupled with the wet film thickness deviation. Its positive or negative sign indicates whether the drying system is enhancing or weakening the solvent evaporation at that point, thereby forming a suppression field that antagonizes the activation field.

[0023] S3 extracts the wet film thickness sequence of each spatial discrete point in the width direction from the fused data volume within a preset time window. The time window length covers several times the product of the production line running speed and the characteristic time of the drying cycle. By performing multifractal detrending fluctuation analysis on the wet film thickness sequence, including subtracting the mean of the entire sequence from each value of the wet film thickness sequence, and then accumulating the values ​​one by one starting from the first value, a cumulative deviation sequence reflecting the degree of cumulative deviation is obtained. In this application, because the original fluctuation of the coating wet film thickness is an oscillation around the benchmark value, its direct autocorrelation structure is difficult to distinguish between true long memory and short-range artifacts. Therefore, after being converted into a cumulative deviation sequence, the persistent deviation in the original sequence is manifested as a long-range trend in the cumulative sequence, while random perturbations are averaged out, making multi-scale scaling behavior easier to detect. The cumulative deviation sequence is divided into equal parts according to a time scale that increases in multiples from a preset minimum scale until it does not exceed a preset proportion of the total length of the sequence. Based on each time scale, the cumulative deviation sequence is divided into several non-overlapping segments of equal length. If there are any remaining segments at the end that are not enough to form a complete segment, the sequence is divided in reverse order from the end of the sequence to ensure that all data points are utilized. Since the film thickness is affected not only by random disturbances, but also by the macroscopic trends of gradual changes in vehicle speed, room temperature drift, and batch-to-batch viscosity of coating liquid, the cumulative deviation data of each equal-length segment is fitted into a second-order polynomial using the least squares method. The root mean square value of the fitted residual is calculated and used as the local fluctuation magnitude of the equal-length segment. By fitting the internal trend of the segment with a second-order polynomial and removing the residual, these macroscopic slow-drift components can be filtered out, while retaining the fluctuation information generated by microscopic dynamics such as coating leveling, solvent evaporation, and wind impact. Based on the selected wave weighting order, the local wave sizes of all equal-length segments at the same time scale are respectively corresponding to the wave weighting order power. After calculating the average value, the inverse of the corresponding wave weighting order is taken to obtain the wave function value corresponding to the wave weighting order at the time scale. Based on each wave weighting order, the set of points of change of the corresponding wave function value with the time scale is plotted in a double logarithmic coordinate. Weighted least squares linear fitting is used, and the slope of the obtained line is used as the generalized scaling exponent corresponding to the wave weighting order. Thus, this application constructs a generalized scaling exponent for the power law relationship of the wet film thickness fluctuation with the observation scale at the corresponding order. If the exponent changes significantly with the order, the sequence has multifractal characteristics; if it is almost unchanged, it is monofractal, which means that the wave structure is simple. In this process, the correlation between the generalized scaling index and the severity of defects at each order was calculated by offline analysis of the wet film thickness sequences of historical normal batches and batches containing known defects, and the orders with significant correlations were retained as a preset set.

[0024] S2 derives the multifractal singular spectrum from the generalized scaling exponent corresponding to each wave weighting order through Legendre transformation. The singular spectrum width is input into the nonlinear mapping function. By the correspondence between the singular spectrum width of each point in the historical normal interval and the upper limit of the allowable fluctuation of the wet film thickness at the corresponding spatial discrete point, the nonlinear saturated response coefficient of the spatial discrete point is output. The dynamic critical collapse threshold of the spatial discrete point is obtained by adding the absolute value of the deviation of the spectral asymmetry of the multifractal singular spectrum and the corresponding spatial discrete point in the current drying intensity feedback distribution matrix after smoothing and amplitude limiting. When a point is already in a high-load correction state of the drying system, it means that the current wet film deviation has approached or exceeded the normal adjustment range, and the remaining correction margin is small. At this time, only a small additional disturbance may cause the deviation to exceed the tolerance limit of the coating, causing sudden defects such as sagging and stringing. Therefore, this application adds the absolute value of the drying intensity feedback deviation to the threshold, that is, quantifies the currently consumed control resources as the reduction of the additional disturbance resistance of the point, so that the collapse judgment is directly related to the real-time control saturation of the production line.

[0025] In this application, an intermediate quantity called the quality index is calculated for each wave weighting order. The value of the quality index is the wave weighting order multiplied by the corresponding generalized scaling index minus one. For adjacent wave weighting orders, the ratio of the difference in quality index to the difference in wave weighting order is calculated as the singularity index. Using the singularity index and the corresponding wave weighting order, the singular spectrum value is obtained, which is the wave weighting order multiplied by the singularity index minus the quality index. Connect all the points obtained with the singular index as the x-axis and the singular spectrum value as the y-axis to form a curve, and obtain the singular spectrum curve. The width of the singular spectrum curve is the difference between the maximum and minimum values ​​of all singular indices, which is called the singular spectrum width. The spectral asymmetry is a measure of the difference between the descent rate of the left half and the descent rate of the right half of the curve.

[0026] It should also be noted that the singular spectral width corresponds to the multi-scale complexity of coating uniformity. A wide width indicates that multiple fluctuation modes, such as slow drift and sudden jump, coexist at that point, which is a statistical sign of local instability of the coating. The spectral asymmetry indicates the dominance of the fluctuation mode.

[0027] S4 uses the distribution matrix of local deviation of wet film thickness as the activation value of the coating state activation field and the distribution matrix of drying intensity feedback as the activation value of the coating state suppression field. Each spatial discrete point corresponds to a node in the dynamic topological directed graph. In each time iteration step, an anisotropic diffusion operation is performed, including: based on the coating state activation field, each node diffuses to the downstream neighbor node connected along the forward material transfer edge. The diffusion flux is equal to the edge weight multiplied by the difference between the activation value of this node and the activation value of the neighbor node. If the difference is positive, the activation value flows out from this node; if it is negative, it flows in from the neighbor node. This updates the activation value of each node. The principle is that in the process of the substrate, the area of ​​local thickness of wet film will migrate downstream longitudinally due to the flow parallelism of the coating itself and the airflow shearing effect of the hot air in the subsequent oven. During the migration, the excess coating will gradually spread or redistribute. The edge weight controls the amount of migration and is modulated by the equipment status and production rhythm. This simulates the effectiveness of this longitudinal migration under different working conditions. Based on the coating state suppression field, each node is diffused in reverse to the upstream node connected along the reverse control coupling edge. The diffusion flux is equal to the weight of the reverse edge multiplied by the difference between the suppression value of this node and the suppression value of the upstream node, and the suppression value of each node is updated. After diffusion is complete, all nodes are traversed. When the activation value of any node exceeds the dynamic critical collapse threshold, the excess deviation of the activation value exceeding the dynamic critical collapse threshold is calculated. The excess deviation is distributed to downstream neighboring nodes according to the weight ratio of all forward material transmission edges of the corresponding node and superimposed on the activation value of the neighboring nodes. The detection is then re-executed for the neighboring nodes that receive the superimposed excess deviation. If their activation value exceeds their own dynamic critical collapse threshold, secondary collapse is triggered and the distribution and suppression of jumps are repeated until the activation values ​​of all nodes are lower than their respective dynamic critical collapse thresholds. After the collapse detection is completed, the activation values ​​of each node are extracted and arranged into a two-dimensional matrix according to the spatial discrete point order to form the abnormal propagation heat map of the coating state at the current moment.

[0028] S4 is based on the absolute values ​​of the activation values ​​of all discrete spatial points in the heat map of abnormal propagation of coating state to form a non-negative sequence. After normalizing the non-negative sequence, it is transformed into a probability distribution. The non-extensive parameter is determined by maximizing the ratio of inter-class distance to intra-class variance of heat map samples of historical normal and abnormal working conditions. The non-extensive parameter is raised to the power of each probability value in the probability distribution. All the obtained values ​​are summed to obtain the sum. The difference between the sum and the non-extensive parameter minus one is obtained by subtracting one from the sum. The non-extensive entropy value is obtained. Because the non-extensive entropy adjusts the sensitivity to extreme probabilities through the power scaling parameter, isolated bright paths can significantly increase the overall entropy value. Therefore, this application provides early warning of sudden coating defects through non-extensive entropy. Based on the progress factor read from the fused data body at the current moment, it is compared with the non-extensive entropy value through the quantile threshold of normal fluctuation of non-extensive entropy under different progress factor intervals. The quantile threshold is constructed by offline self-sampling of high confidence upper bounds from historical data of the same type and speed segment. When the extensive entropy exceeds the quantile threshold corresponding to the current progress factor, the corresponding risk level is output, including slightly exceeding the corresponding attention level and significantly exceeding the corresponding intervention level.

[0029] Based on risk level, S4 selects the node with the most cumulative collapses from the collapsed nodes as the end of the propagation chain. It traces upstream adjacent nodes one by one in the reverse direction of the forward material transfer edge of the dynamic topology directed graph. By statistically analyzing the cumulative collapse count of each node and the average magnitude of the excess deviation at each collapse, since the defect propagation direction of the thermal paper production line is consistent with the substrate running direction, the collapse signal is always transmitted from upstream to downstream level by level. The node with the highest cumulative collapse count and the suppression feedback lags behind the growth of the activation value is marked as a suspected initial instability source. The stored production status information of the day is retrieved. If the key node position on the backtracking path coincides with the product switching timestamp, the anomaly is found to be caused by batch difference of coating liquid.

[0030] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0031] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0032] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for real-time monitoring of a thermal paper coating production line, characterized in that: The specific steps include the following: S1. After aligning the timestamps of the sensor signals acquired by the multi-sensor modules, a two-dimensional process variable matrix is ​​formed. The production progress information and progress factor of the day are added to the side of the two-dimensional process variable matrix to form a fused data body. S2. Based on the material flow direction and energy coupling path of the production line, a dynamic topological directed graph is formed by assigning initial weights and determining the effective feedforward gain based on the progress factor. S3. Based on the row vector of wet film cross section thickness distribution in the fused data volume, the local deviation distribution matrix of wet film thickness is formed by difference calculation. Combined with the hot air temperature and wind speed alignment values ​​applied to spatial discrete points by each drying zone, it is converted into a drying intensity feedback distribution matrix. By introducing multifractal detrending fluctuation analysis, the singular spectrum width is input into the nonlinear mapping function to obtain the nonlinear saturation response coefficient and dynamic critical collapse threshold corresponding to each spatial point. S4. Based on the distribution matrix of local deviation of wet film thickness as the initial value of the coating state activation field and the distribution matrix of drying intensity feedback as the initial value of the coating state suppression field, anisotropic diffusion is performed. After each diffusion is completed, collapse detection is performed by using the linear saturation response coefficient and the dynamic critical collapse threshold. After iterative loop, the final coating state abnormal propagation heat map is obtained. S5. Based on the absolute values ​​of the activation values ​​of all spatial points in the heat map of abnormal propagation of coating state, a non-negative sequence is formed. After being converted into a probability distribution, the risk classification is completed by calculating the non-extensive entropy, and the root cause of the anomaly is located based on the risk classification results.

2. The method for real-time monitoring of a thermal paper coating production line according to claim 1, characterized in that: S1 aligns the sensing signals acquired by the multi-sensor modules according to a unified timestamp, unifies the time base to the frame pulse generated by the trigger sensor at the oven inlet, and extracts a time section according to the sampling time. The continuous variables distributed along the width direction at each time section are expanded into row vectors according to spatial discrete points, and the row vectors of adjacent time sections are stacked in chronological order to form a two-dimensional process variable matrix. Based on the manufacturing execution system, read the daily production progress information; based on the equipment control system, read the real-time status words of the overall equipment; and map the ratio of the remaining total length to be coated to the running time to the progress factor. Each binary bit value of the overall real-time status word of the progress factor is appended to the side of the two-dimensional process variable matrix of each time segment to form a three-dimensional tensor block. The three-dimensional tensor blocks of all time segments are arranged in time sequence to form a fused data volume.

3. The method for real-time monitoring of a thermal paper coating production line according to claim 1, characterized in that: S2 abstracts the functional workstations into graph nodes based on the material flow direction and energy coupling path of the thermal paper coating production line; Between adjacent nodes with material transfer relationships, a forward material transfer edge is established with the direction consistent with the direction of substrate travel. Between the downstream detection station and the upstream adjustment station, a reverse control coupling edge is established with the direction pointing from the detection station back to the adjustment station.

4. The method for real-time monitoring of a thermal paper coating production line according to claim 1, characterized in that: S2 assigns an initial weight to each directed edge and, by reading the overall real-time device status word in the fused data body, applies a decay to the initial weight of the relevant edges according to the preset device status. It reads the progress factor in the fused data body, multiplies the weights of all reverse control coupling edges by one minus the progress tension factor product, and completes the final assignment of each edge weight. It recalculates the edge weights of each edge based on the current device status word and progress factor at each time segment, and outputs the current adjacency matrix and edge weight vector, which together form a dynamic topological directed graph.

5. The method for real-time monitoring of a thermal paper coating production line according to claim 1, characterized in that: S3 extracts the wet film cross-sectional thickness distribution row vector from the two-dimensional process variable matrix at the current moment based on the fused data volume, and extracts the wet film thickness value of the corresponding spatial discrete point under the same variety in multiple stable production periods based on each spatial discrete point of the wet film cross-sectional thickness distribution row vector, and uses the median value as the reference value of the wet film thickness of the spatial discrete point. Subtract the corresponding wet film thickness reference value from the wet film thickness value of each spatial discrete point in the row vector at the current time to obtain the wet film thickness deviation at the point. When there is a point where the wet film thickness deviation is negative, arrange the differences of all spatial discrete points in the original spatial order to form a distribution matrix of local deviation of wet film thickness. Based on each spatial discrete point, the hot air temperature and wind speed values ​​applied by each drying zone to the spatial discrete point are extracted. Based on the evaporation intensity mapping, the equivalent evaporation driving force value is obtained. The equivalent evaporation driving force of all drying zones to the spatial discrete point is summed and the difference is calculated with the evaporation driving force benchmark value of the spatial discrete point under the historical stable production period to obtain the drying intensity feedback deviation of the spatial discrete point. The drying intensity feedback deviation of all points is arranged in spatial order to form a drying intensity feedback distribution matrix.

6. The method for real-time monitoring of a thermal paper coating production line according to claim 5, characterized in that: S3 extracts the wet film thickness sequence of each spatial discrete point within a preset time window from the fused data volume based on each spatial discrete point in the width direction. By performing multifractal detrending fluctuation analysis on the wet film thickness sequence, including subtracting the mean of the entire sequence from each value of the wet film thickness sequence, and then accumulating the values ​​one by one starting from the first value, a cumulative deviation sequence reflecting the degree of cumulative deviation is obtained. The cumulative deviation sequence is divided into several non-overlapping equal-length sub-segments based on a time scale that increases in multiples from a preset minimum scale until it does not exceed a preset proportion of the total length of the sequence. The cumulative deviation data of each equal-length sub-segment is fitted into a second-order polynomial using the least squares method, and the root mean square value of the fitting residual is calculated and used as the local fluctuation magnitude of the equal-length sub-segment. Based on the selected wave weighting order, the local wave sizes of all equal-length segments at the same time scale are respectively corresponding to the wave weighting order power. After calculating the average value, the inverse of the corresponding wave weighting order is taken to obtain the wave function value corresponding to the wave weighting order at the time scale. Based on each wave weighting order, the set of points where the corresponding wave function value changes with the time scale is plotted in a double logarithmic coordinate system. Weighted least squares straight line fitting is used, and the slope of the obtained straight line is used as the generalized scaling exponent corresponding to the wave weighting order.

7. The method for real-time monitoring of a thermal paper coating production line according to claim 1, characterized in that: The S2 derives the multifractal singular spectrum from the generalized scaling exponent corresponding to each wave weighting order through Legendre transformation, inputs the singular spectrum width into the nonlinear mapping function, and outputs the nonlinear saturated response coefficient of the spatial discrete point by the correspondence between the singular spectrum width of each point in the historical normal interval and the upper limit of the allowable fluctuation of the wet film thickness at the corresponding spatial discrete point. The dynamic critical collapse threshold of the spatial discrete point is obtained by adding the absolute value of the spectral asymmetry of the multifractal singular spectrum and the deviation of the corresponding spatial discrete point in the current drying intensity feedback distribution matrix after smoothing and amplitude limiting.

8. The method for real-time monitoring of a thermal paper coating production line according to claim 1, characterized in that: The S4 uses the distribution matrix of local deviation of wet film thickness as the activation value of coating state activation field and the distribution matrix of drying intensity feedback as the activation value of coating state suppression field. Each spatial discrete point corresponds to a node in the dynamic topological directed graph. In each time iteration step, an anisotropic diffusion operation is performed, including: based on the coating state activation field, each node diffuses to the downstream neighbor nodes connected along the forward material transfer edge. Based on the coating state suppression field, each node is diffused in reverse to the upstream node connected along the reverse control coupling edge. After diffusion is complete, all nodes are traversed. When the activation value of any node exceeds the dynamic critical collapse threshold, the excess deviation of the activation value exceeding the dynamic critical collapse threshold is calculated. The excess deviation is distributed to downstream neighboring nodes according to the weight ratio of all forward material transmission edges of the corresponding node and superimposed on the activation value of the neighboring nodes. The detection is then re-executed on the neighboring nodes that receive the superimposed excess deviation until the activation values ​​of all nodes are lower than their respective dynamic critical collapse thresholds. After the collapse detection is completed, the activation values ​​of each node are extracted and arranged into a two-dimensional matrix according to the spatial discrete point order to form the abnormal propagation heat map of the coating state at the current moment.

9. The method for real-time monitoring of a thermal paper coating production line according to claim 8, characterized in that: S4 is based on the absolute values ​​of the activation values ​​of all discrete spatial points in the abnormal propagation heatmap of the coating state to form a non-negative sequence. The non-negative sequence is normalized and transformed into a probability distribution. The non-extensive parameter is determined by maximizing the ratio of inter-class distance to intra-class variance of historical normal and abnormal working condition heatmap samples. The non-extensive parameter is raised to the power of each probability value in the probability distribution. The sum of all the calculated values ​​is obtained. The difference between the sum and the non-extensive parameter minus one is obtained by subtracting one from one to obtain the non-extensive entropy value. The progress factor at the current moment is read from the fused data body and compared with the non-extensive entropy value through the quantile threshold of normal fluctuation of non-extensive entropy under different pre-stored progress factor intervals. When the extensive entropy exceeds the quantile threshold corresponding to the current progress factor, the corresponding risk level is output.

10. A real-time monitoring method for a thermal paper coating production line according to claim 9, characterized in that: S4, based on risk level, selects the node with the most cumulative collapses from the collapsed nodes as the end of the propagation chain. It then traces upstream adjacent nodes hop by hop in the direction of the forward material transfer edge of the dynamic topology directed graph. By statistically analyzing the cumulative collapse count of each node and the average magnitude of the excess deviation during each collapse on the backtracking path, the node with the highest cumulative collapse count and the suppression feedback lags behind the growth of the activation value is marked as a suspected initial instability source. The stored production status information for the day is retrieved. If the key node position on the backtracking path coincides with the product switching timestamp, then the anomaly is found to originate from batch differences in the coating liquid.

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