A method and system for predicting and compensating for printing color deviations

Abstract

The present application belongs to the technical field of printing color management, and particularly relates to a printing color deviation prediction compensation method and system. Multi-modal engineering data with time stamps are collected through an online color detection device, a paper and ink detection device, an equipment state sensor and an environment sensor, the data is subjected to time alignment, filtering, missing value processing and normalization, and attention weighted fusion is carried out on the basis of retaining the identification and physical mapping relationship of each engineering variable; a constrained time delay causal diagram is constructed according to the printing process topology and the safety perturbation response data of the actuator, the local effect coefficient and the response time delay are determined, and an actuator-color sensitivity matrix is formed; the compensation amount is solved in combination with the signed color error and the actuator amplitude, the change rate and the process coupling constraint, and the control instruction is issued under the comprehensive response time delay, so as to realize the executable and traceable closed-loop color compensation.

Description

Technical Field

[0001] This invention belongs to the field of printing color management technology, and more specifically, relates to a method and system for predicting and compensating printing color deviation. Background Technology

[0002] Offset printing, gravure printing, flexographic printing, and digital printing are all susceptible to color variations during continuous production processes due to factors such as paper whiteness and moisture content, ink viscosity and temperature, ink roller temperature, printing pressure, water supply, printing speed, and workshop temperature and humidity. These factors can cause measured colors to deviate from standard samples or digital reference values. Existing production lines typically use online spectrophotometry or offline sampling to obtain color differences, followed by operator adjustments to ink keys, ink pumps, temperature control, or pressure parameters. This method relies on operator experience, and the different physical response delays of different actuators can easily lead to repeated adjustments.

[0003] Existing technologies also employ neural networks, empirical databases, or input-output matrices to predict color difference and compensation. However, when using only the comprehensive color difference ΔE as a control variable, since ΔE is a non-negative scalar, it cannot provide the direction of color shift; when multiple engineering variables are directly fused into a single feature vector, the correspondence between each physical quantity and the specific actuator may be lost; at the same time, if constraints such as actuator amplitude, rate of change, and ink-water balance are not considered, the calculation results may not be applicable to actual printing equipment.

[0004] Furthermore, there are both series and parallel interaction paths among paper, ink, environment, equipment status, and printing results. For example, ink roller temperature can first affect ink viscosity, and then ink transfer rate and color density; water supply and printing speed may also jointly affect the ink-water balance. Using only a single input-output regression model is insufficient to distinguish intermediate processes, and different paths have different response times. Directly treating observed correlations as causal relationships may lead to incorrect control directions due to synchronous feedback or hidden factors.

[0005] To address the aforementioned technical problems, this invention provides a method and system for predicting and compensating printing color deviation. Summary of the Invention

[0006] In view of the problems mentioned in the background art above, the present invention provides a printing color deviation prediction and compensation method and system.

[0007] On one hand, the technical solution adopted by the present invention is as follows: a method for predicting and compensating printing color deviation, comprising the following steps: Step S1, acquiring multimodal data of the printing process through a multimodal sensor group set on the printing production line, wherein the multimodal data includes printing image color data, paper characteristic data, ink characteristic data, equipment operating parameter data, and environmental parameter data; Step S2, performing time alignment, noise filtering, missing value processing, and normalization on the multimodal data to generate multimodal preprocessed data including the time series of variables after preprocessing of each acquisition process variable; calculating the attention weight of each modal data respectively, and performing weighted fusion according to the preset variable order to form a fusion state vector that retains the sensor source, detection area or ink area identification, and physical unit mapping relationship; Step S3, based on the variable time series of the multimodal preprocessed data, the fusion state vector, the printing process topology, and the perturbation response data of the actuator within the safe adjustment range, constructing a color deviation time delay causal graph model constrained by the printing process topology, and determining the local of each directed edge. The process involves: Step S4, identifying key factors affecting printing color deviation and their paths of action based on at least two signed color error components between the current color state and the target color standard; Step S5, multiplying the local effect coefficients of each compensation execution variable's path to each color error component and summing the parallel paths to form an actuator-color sensitivity matrix; Solving for the adjustment amount of each compensation execution variable under the coupling constraints of actuator amplitude, rate of change, and printing process to generate a color compensation strategy; Step S6, determining the timing of control command issuance based on the comprehensive response delay corresponding to each compensation execution variable, outputting equipment operating parameter adjustment commands to the corresponding actuator through the control interface of the printing equipment, and executing the color compensation operation; Step S7, acquiring the compensated printed image color data through an online color detection device and verifying the compensation effect; When the color deviation still exceeds the preset threshold and the data distribution does not change significantly, updating the local effect coefficients and iteratively executing steps S4 to S5; When the data distribution changes significantly, iteratively executing steps S8 to S5.

[0008] Furthermore, the multimodal sensor group includes: an online color detection device, selected from at least one of an online spectrophotometer, a multispectral camera, or an industrial camera calibrated with a standard color chart, for collecting the colorimetric and density values ​​of printed matter; a paper characteristic detection device, for collecting at least one of paper whiteness, moisture content, smoothness, and thickness; an ink characteristic detection device, for collecting at least one of ink viscosity, ink temperature, and ink color density; an equipment status sensor, for collecting at least two of ink supply, ink key opening, ink roller temperature, printing pressure, water supply, printing speed, and actual output of the actuator; and an environmental sensor, for collecting workshop temperature and relative humidity.

[0009] Furthermore, the preprocessing in step S2 includes: time alignment of multimodal data with different sampling frequencies using a linear interpolation method based on a unified time reference benchmark; noise filtering using differentiated filtering strategies for the noise characteristics of different modal data; missing value completion using a regression completion method based on multimodal correlation, marking the data segment as unusable when the missing rate of a certain modality exceeds a preset threshold; and normalizing the multimodal data by uniformly mapping it to a preset numerical range.

[0010] Further, in step S2, the preprocessed features of each modality are first mapped by the corresponding linear projection layer to modal feature vectors of a preset dimension for unifying the dimension and subsequent attention weighting; the preset attention network outputs scalar attention scores for each modality, and the weight parameters of the attention network are predetermined and stored in a fixed manner through offline training; each attention score is converted into the weight of each modality by the softmax function, and the weighted modal feature vectors are concatenated in a preset order to form the fusion state vector, and a mapping table between the feature coordinates in the modal feature vector and the fusion state vector and the corresponding acquisition engineering variables or variable groups is established simultaneously.

[0011] Furthermore, step S3, constructing the color deviation causal graph model, specifically includes: determining a set of candidate variables related to color deviation based on the mapping table corresponding to the fusion state vector; the set of candidate variables includes uncontrollable perturbation variables, compensation execution variables, printing process state variables, and color error variables; based on the historical operating data of the candidate variable set and the safety perturbation response data of the actuator, constructing a directed acyclic graph structure using a data-driven structural search algorithm combined with scoring criteria, and limiting the allowed directions of directed edges through printing process topological constraints; for directed edges connected to compensation execution variables, determining the local effect coefficient based on the local response slope before and after the corresponding safety perturbation; for other directed edges, determining the local effect coefficient based on the partial derivative of the conditional expectation function of the variable and its parent node set; using the color error variable as the target variable, identifying directed paths pointing to the target variable, using the product of the local effect coefficients on each path as the path influence, and identifying key factors based on the path influence, outputting the color deviation causal analysis results including a list of key factors, contribution ranking, and description of the action path.

[0012] Furthermore, the printing process topology constraints include: uncontrollable disturbance variable nodes are only allowed to point to printing process state variable nodes or color error variable nodes; compensation execution variable nodes are only allowed to point to printing process state variable nodes that can be physically adjusted by the corresponding actuator; the direction of the directed edges between printing process state variable nodes is limited according to the paper transport direction, ink transfer order, or energy transfer order; in the color deviation time delay causal graph model, color error variable nodes are not used as parent nodes of compensation execution variable nodes.

[0013] Furthermore, each directed edge is associated with a response delay parameter, which is determined by the cross-correlation or transfer entropy of the variable time series and verified by the safety perturbation response data of the corresponding actuator. When the recent multimodal data is determined to have changed significantly after distribution testing, the graph structure is relearned in the state of stopping the automatic issuance of new compensation instructions or running in shadow model, and the current model is replaced after verification.

[0014] Further, step S4 specifically includes: determining the deviation between the current color state and the target color standard based on the color deviation cause analysis results, wherein the deviation includes at least two signed color error components; selecting one or more variables from the controllable variables of the printing equipment that have an effective action path with at least one color error component and whose total path gain absolute value reaches the minimum controllable threshold as compensation execution variables; multiplying the local effect coefficients on each action path from each compensation execution variable to each color error component, and summing the parallel path gains connecting the same compensation execution variable and the same color error component to form an actuator-color sensitivity matrix; solving the adjustment amount of each compensation execution variable under the constraints of actuator amplitude, rate of change, and printing process coupling based on the predicted color error at the target observation time, the actuator-color sensitivity matrix, and the execution cost; integrating the adjustment amounts of each compensation execution variable into a structured color compensation strategy, wherein the color compensation strategy includes a list of equipment parameters to be adjusted, the adjustment direction and magnitude of each parameter, the execution sequence, and the priority.

[0015] Furthermore, in step S5, the response delays on each action path are accumulated to obtain the path response delay, and the path response delays of the same compensation execution variable are weighted according to the absolute value of the path gain to obtain the comprehensive response delay. Based on the target observation time, the compensation execution variable with a longer comprehensive response delay receives the control command first, and the compensation execution variable with a shorter comprehensive response delay receives the control command later, so that the main compensation effects of different actuators act on the printed matter together near the target observation time.

[0016] Secondly, the present invention provides a printing color deviation prediction and compensation system, including a multimodal sensor group, an industrial computer or edge server, a printing equipment control interface, and an actuator connected to the printing equipment control interface; the industrial computer or edge server includes: a data acquisition module, used to acquire time-stamped printing image color data, paper characteristic data, ink characteristic data, equipment operating parameter data, and environmental parameter data through the multimodal sensor group; a data preprocessing and fusion module, used to perform time alignment, noise filtering, missing value processing, and normalization on the multimodal data, and to perform weighted splicing of each modal feature based on a preset attention network to generate a fused state vector that retains the physical mapping relationship of variables; causal reasoning... The system comprises four modules: a color deviation delay causal graph model, a compensation strategy generation module, and a compensation strategy generation module. The first module constructs an actuator-color sensitivity matrix based on variable time series, fused state vectors, printing process topology, and actuator safety perturbation response data. The second module verifies the compensation effect and triggers model updates or iterations based on the compensated printed image color data. The third module outputs equipment operating parameter adjustment instructions to the actuator via the printing equipment control interface based on the comprehensive response delay. The fourth module verifies the compensation effect and triggers model updates or iterations based on the compensated printed image color data.

[0017] The beneficial effects of this invention are:

[0018] By employing signed color error components to preserve the direction of color shift, the system avoids generating control commands with unclear directions directly from non-negative comprehensive color differences. Through the construction of a color deviation causal graph model constrained by the printing process topology, accurate identification and quantitative analysis of the causes of printing color deviation are achieved, providing clear causal basis for compensation decisions and addressing the lack of interpretability inherent in black-box models to some extent. A collaborative architecture of multimodal data fusion and causal reasoning comprehensively considers the coupled influence of multiple factors such as paper, ink, equipment, and environment on color, improving the accuracy of color deviation prediction and the targeting of compensation strategies. Constraints on actuator amplitude, rate of change, and process coupling ensure that the compensation amount can be actually implemented by the printing equipment. Causal path delay alignment control ensures that the main compensation actions of different actuators converge at the same target time, reducing overcompensation or undercompensation caused by different response speeds. The causal graph model is expressed in a structured directed acyclic graph form, supporting model migration and adaptation under different printing equipment and material conditions, reducing system deployment and maintenance costs. Attached Figure Description

[0019] The present invention can be further illustrated by the non-limiting embodiments given in the accompanying drawings;

[0020] Figure 1 This is a flowchart illustrating the printing color deviation prediction and compensation method of the present invention.

[0021] Figure 2 This is a schematic diagram of the architecture of the printing color deviation prediction and compensation system of the present invention. Detailed Implementation

[0022] like Figure 1 As shown, this embodiment provides a method for predicting and compensating printing color deviation, including the following steps:

[0023] Step S1: Acquire multimodal data of the printing process through a multimodal sensor group installed on the printing production line. The multimodal data includes printed image color data, paper characteristic data, ink characteristic data, equipment operating parameter data, and environmental parameter data.

[0024] The multimodal sensor group in this step includes:

[0025] Online color detection device: This can be at least one of an online spectrophotometer, a multispectral camera, or an industrial camera calibrated with a standard color chart. The online spectrophotometer is preferably positioned after the final color group or before the paper delivery section to measure predetermined detection areas in the color control strips or printed images; the industrial camera uses a standard white board and a standard color chart for geometric and color calibration. The color detection device is used to acquire the chromaticity and density values ​​of the printed matter.

[0026] Paper characteristic detection device: including whiteness meter, moisture content sensor, thickness sensor or smoothness detection device, used to collect at least one of paper whiteness, moisture content, smoothness and thickness. For paper parameters that cannot be continuously detected online, they can be detected at the beginning of paper change or batch, and the detection results can be associated with the roll number, paper stack number or paper batch number of that batch.

[0027] Ink property detection device: including a viscometer, temperature sensor, densitometer, or colorimeter, used to collect at least one of ink viscosity, ink temperature, and ink color density. For offset printing, ink temperature and ink supply status can be obtained from the ink fountain, ink supply pipeline, or ink temperature control circuit; for gravure or flexographic printing, viscosity and flow rate can be obtained through feedback from an online viscometer and ink supply pump.

[0028] Equipment status sensors: used to collect at least two of the following: ink supply, ink key opening, ink roller temperature, printing pressure, water supply, printing speed, and actual output of the actuator.

[0029] Environmental sensors: used to collect workshop temperature and relative humidity.

[0030] Specifically, the collection frequency of various types of data is set differently according to modal characteristics: color data and equipment operating parameters are sampled at a high frequency of once every 0.5 seconds, environmental parameters are sampled at a medium frequency of once every 30 seconds, and paper and ink characteristic data are sampled at a low frequency of once per batch. All data carries a timestamp in a uniform format and is transmitted to the system host via industrial Ethernet. Each piece of data has at least the device identifier, detection area or ink area identifier, sampling time, physical unit, calibration version, and validity identifier.

[0031] Step S2: Preprocess the multimodal data to generate multimodal preprocessed data with a unified structure; calculate the attention weight of each modal data based on a preset attention network, and weight and concatenate the modal features according to the preset variable order to generate a fusion state vector that retains the original engineering variable mapping relationship.

[0032] Since different sensors have different sampling periods, the moment the printed sheet arrives at the online color detection position is taken as the color observation moment. The time the corresponding printed sheet passes through each upstream station is determined based on the printing speed, sensor installation distance, and encoder pulses. Based on a unified time reference, a linear interpolation method is used to synchronize the time of multimodal data with different sampling frequencies. For missing values ​​of mode m at time t, the observation values ​​at its adjacent time points t1 and t2 are used. and Calculate the interpolation using the following formula:

[0033]

[0034] Where m is the sensor or engineering variable number; t is the time to be aligned; and For adjacent valid sampling times, and < t < .like = If any endpoint is invalid or the gap exceeds the maximum interpolation interval, no interpolation will be performed, and the corresponding variable for that sample will be marked as missing. The batch-type paper or ink parameters will retain the most recent valid value within their batch validity period.

[0035] Different filtering strategies are employed to address the noise characteristics of data from different modalities. For color data and equipment operating parameters, median filtering is used to remove impulse noise; for environmental parameters, an exponentially weighted moving average method is used to smooth short-term fluctuations, with a smoothing coefficient λ ranging from 0.2 to 0.3.

[0036] Then, a linear regression completion method based on multimodal association was adopted. The other modality data with the highest correlation with the missing data was used as the independent variable to build a univariate linear regression model to predict the missing value. When the missing rate exceeds 30%, the data is marked as unavailable and re-collection is triggered.

[0037] Then, normalization is performed, and an effective lower limit obtained from calibration is set for each sensor. and effective upper limit Scaling value used for model calculation Obtained by the following formula: .

[0038] in, These are the actual measured values ​​of the project quantity; and To define the valid range; ε prevents positive numbers with zero denominators; clip(·,0,1) restricts the result to 0 to 1. When - If the value is less than ε, the sensor calibration is deemed invalid and will not be used for model updates. The scaling parameters are saved in the model and converted back to engineering units when outputting control values.

[0039] Outlier handling prioritizes sensor self-diagnosis, range verification, and rate of change verification. If the change of a variable within a single sampling period exceeds the maximum rate of change achievable by the device, that point is marked as suspicious. If multiple consecutive sampling points are suspicious, model updates related to that variable are frozen, and calibration or maintenance is prompted. Large control commands must not be continued to be output simply by truncating outliers.

[0040] After the above preprocessing, the preprocessed features of each modality are first mapped by their respective linear projection layers to modal feature vectors hi (i=1,2,...,M, where M is the total number of modalities, M=5 in this embodiment; each modality has the same dimension after projection, all being d-dimensional), generating multimodal preprocessed data with a unified structure. Subsequently, the attention score of each modality data is calculated through a preset attention network. This attention network is a single-layer fully connected network, and its weight matrix is... and bias vector Offline training was pre-determined—2000 training samples containing data for each modality and corresponding color deviation values ​​were collected. The optimization objective was color deviation prediction accuracy. The Adam optimization algorithm was trained for 100 epochs until the loss function converged. After training, [the data was then processed]. and The information is permanently stored in the system. Attention scores are calculated using the following formula:

[0041] in Let i be the preprocessed feature vector of the i-th mode. Here is the weight matrix of the attention network. The bias vectors are both determined through offline training. ReLU is the activation function max(0,x). Then, the attention scores are converted into weights for each modality using the softmax function.

[0042] Where αi is the scalar attention score of the i-th modality, wi is the normalized attention weight of the i-th modality, M is the total number of modalities, and exp is the natural exponential function; wi ranges from 0 to 1 and Σwi=1, and the weights are calculated by the attention network from the modal features of the current sample, not by manually fixed coefficients. Finally, the preprocessed feature vectors of each modality are concatenated according to their weights to generate a unified fusion state vector (denoted as H), and a mapping table is simultaneously established between the feature coordinates in the modal feature vector and the fusion state vector and the corresponding acquisition engineering variables or variable groups:

[0043] The fusion state vector (denoted as H) integrates five key information categories: color, paper, ink, equipment, and environment. It serves as the data input for the subsequent causal inference module. Since the feature vector reflects the actual multimodal state of the current sample, the attention score and weight of each modality change online with the input sample. Therefore, the attention network dynamically assigns weights to each modality based on its contribution to the current color deviation during inference, rather than using fixed equal weights or manually setting weights. This is precisely the role of the attention mechanism: automatically highlighting one or more modalities that carry the strongest signal of the current color deviation to suppress noisy modalities, improve fusion quality, and at the same time keep the network parameters fixed and stored to maintain the consistency of system behavior.

[0044] Step S3: Based on the variable time series, fused state vector, printing process topology, and actuator safety perturbation response data of the multimodal preprocessed data, construct a color deviation time delay causal graph model, identify the key factors affecting printing color deviation and their action paths, and output the color deviation cause analysis results.

[0045] Specifically, it includes:

[0046] Based on the preprocessed time series of each acquired engineering variable in the multimodal preprocessed data, and referring to the mapping table corresponding to the fused state vector H, a set of candidate variables V related to color deviation is determined. Since the fused state vector H is formed by concatenating each weighted modal feature vector in a preset order, the mapping table records the source correspondence between each modal feature component, projected feature coordinates, and the corresponding acquired engineering variables, variable groups, or derived variables. When the linear projection layer uses variable-wise mapping or grouped mapping, it records the corresponding original variables or variable groups and mapping parameters. The candidate variable set V is selected from the time series of acquired engineering variables or derived variables with clear physical meaning. The mapping table is used to confirm the source relationship between the corresponding variables and the modal feature vector and the fused state vector, rather than recovering the engineering variables from the concatenated fused state vector. Candidate variables include: paper whiteness deviation value X. paper Ink viscosity deviation value X ink Change in printing speed X speed Ink roller temperature deviation value X temp Environmental humidity deviation value X humidity Ink transfer rate X transfer Network expansion value X dotgain Ink-water balance value X balance The variables, such as chromaticity deviation value Y, are expressed in time series form.

[0047] Among these variables, paper, ink, equipment, and environmental variables can be directly obtained from their respective sensors; ink transfer state values ​​can be calculated from solid color patch density, ink supply, printing pressure, and printing speed using equipment calibration relationships; dot gain values ​​can be calculated based on the density of halftone dots and solid color patches using the Murray-Davies relationship, or by segmenting the halftone area using a calibrated camera; and ink-water balance values ​​can be calculated based on the ratio of water supply to ink supply, reflectivity of non-image areas, and the fluctuation of color density across consecutive printed sheets using pre-calibrated mapping relationships. All derived variables retain the original quantities and calibration versions used in the calculations for traceability.

[0048] The chromaticity deviation value Y is the target variable, which includes ΔL*, Δa*, and Δb* components.

[0049] For each detection region r, obtain the reference color value ( , , ) and measured color values ​​(L* r (t), a* r (t), b* r (t)). The signed color error vector for control is:

[0050]

[0051]

[0052] The overall color difference is calculated using the CIE 1976 color difference formula:

[0053] This is only used to determine whether the detection area is within the allowable tolerance. The compensation direction is determined by the signs of ΔL*, Δa*, and Δb* and the actuator-color sensitivity relationship.

[0054] During equipment calibration or when production is stable and color difference is within a safe range, a safety perturbation is applied to each of the automatically adjustable actuators. The magnitude of the safety perturbation does not exceed 5% of the actuator's allowable adjustment range, preferably 1% to 3%, and simultaneously meets the equipment's specified rate of change limit. When a perturbation is applied to one actuator, the remaining actuators maintain their current settings or are only allowed to fluctuate within a preset narrow range. The printing process state variables and signed color error responses before and after the perturbation are recorded to verify the directed edge direction, estimate the local response slope, and determine the response delay. Compensation actuator variable paths that do not receive stable perturbation response support are not used for automatic compensation.

[0055] A causal graph model with a directed acyclic graph structure is constructed by combining a score-based structure search algorithm with the Bayesian information criterion, where directed edges represent direct causal dependencies between variables.

[0056]

[0057] Wherein, the variable set V = {v1, v2, ..., v n The features are taken from the multimodal preprocessed data generated in step S2. Represents the variables in the causal graph G. The set of all direct parent node variables is determined by the GES algorithm combined with the BIC score. Specifically, the GES algorithm starts from an empty graph and sequentially performs forward edge addition search and backward edge deletion search, with each edge operation aiming to maximize the improvement of the BIC score, eventually converging to a locally optimal graph structure. BIC is the Bayesian information criterion scoring function, calculated based on the conditional probability distribution of each variable and its parent node set, BIC=-2·ln(L)+k·ln(N), where L is the maximum likelihood function of the data under the current graph structure, k is the number of model parameters, and N is the sample size.

[0058] To enhance the robustness of causal discovery, a stability selection strategy based on Bootstrap is introduced: the original data is resampled 100 times with replacement, and the above causal structure learning is performed respectively. The proportion of the occurrence of each directed edge in the 100 learning results is counted, and only causal edges with a frequency ≥ 0.8 are retained. The remaining edges are considered unstable relationships and removed from the causal graph.

[0059] The edge set of the causal graph model is constrained by the printing process topological constraints, specifically including:

[0060] Uncontrollable disturbance variable nodes, such as ambient humidity and paper moisture content, are only allowed to point to printing process state variable nodes or color error variable nodes;

[0061] Compensation execution variable nodes, such as ink supply, ink roller temperature, printing pressure, water supply, and printing speed, are only allowed to point to printing process state variable nodes that can be physically adjusted by the corresponding actuator;

[0062] The direction of the directed edges between the state variable nodes in the printing process is defined according to the paper feeding direction, ink transfer sequence, or energy transfer sequence.

[0063] Color error variable nodes are not allowed to be parent nodes of compensation execution variable nodes, meaning that causal edges returning from color error to execution variables are not permitted, in order to distinguish between the physical process model and the controller feedback logic.

[0064] For example, the ink roller temperature control value can indicate the ink temperature or viscosity state; the ink supply quantity can indicate the ink transfer rate or color density state; the water supply quantity can indicate the ink-water balance state; and the printing pressure can indicate the ink transfer rate or dot gain state. Ambient humidity and paper moisture content can indicate ink-water balance or paper condition. The above relationships only define the permissible directions; whether a particular device retains this edge, its sign, and its size are all determined by calibration data.

[0065] After the causal graph structure is determined, a local effect coefficient is assigned to each directed edge. For directed edges whose starting point is the compensation execution variable, The local slopes of the changes in the outcome variable and the causal variable during the safe perturbation process are preferred for determination, and robust statistical values ​​are obtained through multiple positive and negative perturbations. For the remaining directed edges, a conditional expectation function of the outcome variable with respect to its parent node set is fitted using multiple regression, and the partial derivative of this conditional expectation function with respect to the causal variable is used to determine the outcome variable. .

[0066] The larger the absolute value of the local effect coefficient, the stronger the marginal influence of the causal variable on the outcome variable, assuming other parent nodes remain unchanged. A positive local effect coefficient indicates a unidirectional effect, while a negative coefficient indicates a unidirectional effect. For edges with significant nonlinearity, piecewise linear or local polynomial fitting can be used near the current working point, and the corresponding working interval and coefficients can be stored together.

[0067] For any path p pointing from a given initial variable to the color deviation target variable Y, the product of all local effect coefficients along that path is defined as the path influence δ. p The starting variables corresponding to paths whose absolute value of influence exceeds a preset threshold are identified as candidate key factors.

[0068] When there are multiple parallel paths from the same starting variable to the same color error component, the total influence δ of the starting variable is obtained by summing the influence of each path by sign. total For a path set P(u,Y), the absolute value of the path influence is used as a weighting factor, and the overall path stability is defined as follows: Define the comprehensive perturbation verification value as , where ε is a positive number to prevent the denominator from being zero. Path stability is used to quantify the reliability of each causal edge contained in path p during structure learning, and is defined as the minimum value of the stability index of all directed edges on the path: The edge stability index freq(e) is taken from the frequency of the directed edge in the aforementioned Bootstrap stability selection during 100 resampling learning cycles with replacement. Edges with a frequency ≥ 0.8 are considered stable edges and are retained in the causal graph. The closer stab(p) is to 1, the more stable and reliable the path is in multiple resampling cycles. The perturbation verification value verif(p) is used to quantify whether the direction and magnitude of the path p have been confirmed by safe perturbation measurement: when the sign of the path prediction response and the safe perturbation measurement response are consistent and the relative error of the amplitude does not exceed the preset tolerance η, verif(p) = 1; when the signs are consistent and the relative error of the amplitude is greater than η but not more than 2η, verif(p) = 0.5; when the signs are inconsistent or the relative error of the amplitude exceeds 2η, verif(p) = 0, where η is set offline based on historical calibration data and sensor measurement errors. The contribution ranking is arranged from largest to smallest based on the overall contribution. C(u,Y) is actually sorted using |δtotal(u,Y)|, where the sign of δtotal is still used to retain the direction of action; that is, the initial variables with the largest absolute value of total influence, stable path, and verified by perturbation are prioritized and output as key factors. The preset path influence threshold can be calibrated offline according to the sensor noise level; in this embodiment, a normalized influence of 0.1 can be used.

[0069] Where u represents the candidate starting variable node, specifically corresponding to paper, ink, equipment, or environmental engineering variables; Y represents the target color error variable node, actually represented by one of the components ΔL*, Δa*, or Δb* of the detection region r; P(u,Y) represents the set of all retained directed paths from u to Y after satisfying the printing process topology constraints, causal graph acyclic constraints, Bootstrap stability threshold, and security perturbation verification conditions; δ p The signed influence of path p is equal to the local effect coefficient θ of each directed edge along that path. ij The product of u and y; δtotal(u,Y) represents the algebraic summation of the influence of the same initial variable u on the target variable Y by sign. |δp| in the formula is only used as a weighting factor for path stability and perturbation verification values. verif(p) is the path perturbation verification value, determined based on the sign and magnitude relative error between the predicted path response and the measured safety perturbation response, taking values ​​of 0, 0.5, or 1; η is the magnitude relative error tolerance determined offline based on historical calibration data and sensor measurement errors. The path starting point data in P(u,Y) comes from the corresponding sensor or equipment status records, and the target color error comes from the detection results of an online spectrophotometer, multispectral camera, or calibrated industrial camera.

[0070] The model supports a dynamic update mechanism. When recent data shows a significant change in the distribution of at least one key variable (p < 0.05) according to the Kolmogorov-Smirnov test, the automatic expansion of compensation based on the old structure is stopped, and the graph structure is relearned in the shadow model or under shutdown calibration. The current structure can only be replaced after the new structure has been validated with reserved data and the compensation direction is consistent with the safety perturbation results. When no structure update is triggered, only the local effect coefficients are updated recursively.

[0071] For the above color deviation cause-effect graph model G=(V,E), the node set V represents the engineering variables related to printing color deviation, and the directed edge set E represents the interaction relationships retained within the allowable range of the printing process topology.

[0072] The node set V is divided into four categories: uncontrollable disturbance variables, compensation execution variables, printing process state variables, and color error variables.

[0073] Uncontrollable disturbance variables include paper whiteness, paper moisture content, initial ink viscosity, initial ink temperature, and ambient temperature and humidity;

[0074] The compensation execution variables include ink supply or ink key opening, ink roller temperature setpoint, printing pressure, water supply, and printing speed;

[0075] The state variables in the printing process include ink transfer state value, dot gain value, and ink-water balance value;

[0076] The color error variable is the signed color error component, color deviation value Y, measured by ΔL*, Δa*, and Δb*.

[0077] The cause-effect graph model employs a time-delay structure, meaning that each directed edge is associated with a response delay parameter. The unit is seconds, representing the time interval from the change of the causal variable to the appearance of an observable response in the result variable. For historical operating data, the candidate response delay can be determined based on the lag time corresponding to the stable peak value of the cross-correlation coefficient or the transfer entropy. For directed edges connected to the compensation execution variable, the candidate response delay also needs to be verified by the safety perturbation response curve. If the difference between the two results exceeds the preset tolerance, automatic timing compensation for that edge will not be enabled.

[0078] Step S4: Based on the color deviation cause analysis results and combined with the preset target color standard, generate a color compensation strategy.

[0079] Based on the color deviation cause analysis results, a signed color error vector is determined between the current color state and the target color standard. One or more variables from the adjustable variables of the printing equipment that have an effective path with at least one color error component and whose total path gain absolute value reaches the minimum controllable threshold are selected as compensation execution variables. The minimum controllable threshold is calibrated offline based on the minimum controllable adjustment step size of the actuator and the sensor noise level, representing the lower limit of the path gain corresponding to the smallest effective color change that the actuator can produce that can be distinguished by the color detection device. Variables below this threshold are not practically compensable and are therefore not used as compensation execution variables. For ease of description, the k-th adjustable execution variable node is denoted as u. k Let the r-th color error component node be denoted as e. r For any path p, its local path gain is the product of the coefficients of the local effects along that path.

[0080] Where (i,j) are directed edges on path p; The local effect coefficients corresponding to the directed edges, i.e., the aforementioned Since the engineering units of the coefficients of adjacent sides cancel each other out in sequence, The unit is the error component engineering unit divided by the execution variable engineering unit.

[0081] For connecting the same u k and e r Sum all retained paths to obtain the total path gain:

[0082] Where P(k,r) is the set of paths from uk to er; when there are no effective paths or the absolute value of the total path gain is less than the minimum controllable threshold, let =0, do not choose u k Compensation e r .

[0083] Each Arrange the error components r as rows and the execution variables k as columns to obtain the actuator-color sensitivity matrix J.

[0084] Based on the path from the uncontrollable perturbation variable to the color error variable in the time-delay directed graph, predict the error vector at the target time T without applying this compensation. The compensation amount Δu is solved using the following quadratic objective:

[0085] Wherein, Δu is the column vector of adjustment amounts for each compensation execution variable; Q is the semi-definite color error weight matrix, which is a diagonal matrix, and the diagonal elements are set according to the tolerance requirements of each color error component—the industrial tolerances of ΔL, Δa, and Δb* are ±1.5, ±1.5, and ±1.5, respectively, so the diagonal elements of Q are 1 / tolerance²; R is the positive definite execution cost weight matrix, which is a diagonal matrix, and the diagonal elements are set according to the adjustment cost of each execution variable, with larger diagonal elements corresponding to actuators with higher adjustment costs; λ is the non-negative regularization coefficient, determined in the offline calibration stage using the L-curve method, with a value range of 0.01 to 0.5, and the specific value is optimized and selected during calibration based on the equipment characteristics.

[0086] At least the following actuator amplitude and rate of change constraints should be set:

[0087]

[0088] Where u(t) is the current actual value of the actuator; u min and u max The lower and upper limits allowed by the device; and Δt represents the allowable negative and positive rates of change per unit time; Δt is the control period.

[0089] In addition to actuator amplitude and rate of change constraints, printing process coupling constraints are also set. For example, the ratio of water supply to ink supply is limited to the water-ink balance range obtained by equipment calibration; when the printing pressure adjustment exceeds the preset value, the simultaneous change in printing speed is limited; for multiple ink zones sharing the same ink supply circuit or temperature control circuit, their total adjustment and the adjustment difference between adjacent ink zones are limited. The process coupling constraints can be expressed as linear or piecewise linear inequalities of compensation variables, and participate in the solution of compensation quantities together with actuator constraints.

[0090] The adjustment amounts of each compensation execution variable are integrated into a structured compensation strategy, which includes a list of equipment parameters to be adjusted, the adjustment direction and magnitude of each parameter, and the execution sequence and priority of the adjustment.

[0091] Step S5: According to the color compensation strategy, output the equipment operating parameter adjustment command to the actuator through the control interface of the printing equipment, and perform the color compensation operation;

[0092] The total delay for path p is defined as the sum of the delays of all edges along that path:

[0093] Execution variable u k The target error may be affected by multiple paths, and its overall response delay is weighted by the absolute value of the path gain:

[0094] In the above time delay formula, i and j represent the cause node and the result node in the cause-effect graph, respectively, and (i,j) represents a retained directed edge; The response delay of the directed edge, in seconds, is obtained from variable time series analysis and verified by the security perturbation response curve. P(k) is the cumulative delay of each directed edge on path p; P(k) is the execution variable u. k The set of retained paths for all color error components involved in this control; For execution variable u k The overall response delay is weighted according to the absolute value of the gain of each path. ε in the denominator is a preset positive small quantity used for normalization calculations, only to avoid division by zero when all path gains are zero; it does not represent the physical response of the printing equipment. When P(k) is empty or all paths fail validity, stability, or perturbation verification, it is not calculated. Furthermore, it does not issue automatic compensation instructions to the corresponding implementing agencies.

[0095] Let the target convergence time T be the time from the current decision time t0 to the target observation time when the main compensation effects of all actuators are expected to act together on the printed material, and the value of T shall not be less than the combined response delay of all selected compensation execution variables. The maximum value in. Based on the current decision time t0, at the time t is the time the control instruction for the kth compensation execution variable is issued. k =t0+T− Output the corresponding adjustment instructions. Execution variables with longer response times are executed first, and execution variables with shorter response times are executed later, so that the main compensation effects converge around t0+T.

[0096] Step S6: Obtain the compensated printed image color data through the color detection device and verify the compensation effect. If the color deviation still exceeds the preset threshold, iteratively execute steps S3 to S5.

[0097] After the target observation time is reached, the online color detection device remeasures the corresponding printed sheet or detection area, forming a compensated error vector e. after When the overall color difference of each detection area is within the production standard tolerance, the compensation is considered complete. When the error has not reached the tolerance but has decreased compared to before compensation, and the distribution of key variables has not changed significantly, the local effect coefficients are updated using the recursive least squares method with a forgetting factor, the actuator-color sensitivity matrix J is recalculated, and steps S4 to S5 are iteratively executed. When the distribution changes significantly, the graph structure is relearned and verified according to step S3. Each iteration adheres to actuator constraints, process coupling constraints, and the maximum number of iterations. If the tolerance is still not met after reaching the maximum number of iterations, automatic compensation stops and a prompt is displayed to check the ink, paper, sensor, or mechanical condition.

[0098] In addition, this embodiment also provides a printing color deviation prediction and compensation system, which includes a multimodal sensor group, an industrial computer or edge server, a printing equipment control interface, and an actuator connected to the control interface. The industrial computer or edge server is equipped with a processor and a memory, the memory storing programs executed by the processor to implement the following functional modules:

[0099] The data acquisition module is used to acquire timestamped printed image color data, paper characteristic data, ink characteristic data, equipment operating parameter data, and environmental parameter data through a multimodal sensor group, and to record equipment identification, detection area or ink zone identification, physical unit, calibration version, and validity status.

[0100] The data preprocessing and fusion module is used to perform time alignment, noise filtering, missing value processing and normalization on the multimodal data, and to perform weighted concatenation of each modal feature based on a preset attention network to generate a fused state vector and a variable mapping table.

[0101] The causal reasoning module is used to construct a color deviation delay causal graph model based on variable time series, fused state vector, printing process topology and actuator safety perturbation response data, determine local effect coefficients and response delay, and output key factors and their action paths.

[0102] The compensation strategy generation module is used to form an actuator-color sensitivity matrix based on the local effect coefficients of each action path, and solve the adjustment amount of each compensation execution variable under the coupling constraints of actuator amplitude, rate of change and printing process, to generate a color compensation strategy including equipment parameters, adjustment direction and amplitude, execution sequence and priority.

[0103] The compensation execution and verification module is used to output equipment operating parameter adjustment instructions to the actuator through the printing equipment control interface based on the comprehensive response delay, and to verify the compensation effect based on the compensated printed image color data, so as to trigger the update of local effect coefficients, graph structure relearning, or the next round of compensation.

[0104] This invention does not require all sensors and actuators to be present simultaneously. As long as a calibrable physical action path is formed between at least one signed color error component and an adjustable actuator variable, and the printing process can be actually changed through a control interface, the corresponding subset can be implemented.

[0105] The present invention has been described in detail above. The specific embodiments are provided only to help understand the method and core ideas of the present invention. It should be noted that those skilled in the art can make various improvements and modifications to the present invention without departing from its principles, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

Claims

1. A method for predicting and compensating for printing color deviation, characterized in that: Includes the following steps: Step S1: Acquire multimodal data of the printing process through a multimodal sensor group installed on the printing production line. The multimodal data includes printed image color data, paper characteristic data, ink characteristic data, equipment operating parameter data, and environmental parameter data. Step S2: Perform time alignment, noise filtering, missing value processing, and normalization on the multimodal data to generate multimodal preprocessed data. The multimodal preprocessed data includes the time series of variables after preprocessing for each acquisition engineering variable. Calculate the attention weight of each modality data and perform weighted fusion according to the preset variable order to form a fusion state vector that retains the sensor source, detection area or ink zone identifier, and physical unit mapping relationship. Step S3: Based on the variable time series of the multimodal preprocessed data, the fused state vector, the printing process topology, and the perturbation response data of the actuator within the safe adjustment range, construct a color deviation delay causal graph model constrained by the printing process topology, determine the local effect coefficient and response delay of each directed edge, and identify the key factors affecting printing color deviation and their action paths. Step S4: Based on at least two signed color error components between the current color state and the target color standard, multiply the local effect coefficients of the action paths from each compensation execution variable to each color error component and sum the parallel paths to form an actuator-color sensitivity matrix; solve the adjustment amount of each compensation execution variable under the coupling constraints of actuator amplitude, rate of change and printing process to generate a color compensation strategy. Step S5: Determine the timing of the control command issuance based on the comprehensive response delay corresponding to each compensation execution variable, and output the equipment operating parameter adjustment command to the corresponding actuator through the control interface of the printing equipment to perform the color compensation operation; Step S6: Obtain the compensated printed image color data through an online color detection device and verify the compensation effect; when the color deviation still exceeds the preset threshold and the data distribution does not change significantly, update the local effect coefficient and iteratively execute steps S4 to S5; when the data distribution changes significantly, iteratively execute steps S3 to S5.

2. The printing color deviation prediction and compensation method according to claim 1, characterized in that: The multimodal sensor group includes: An online color detection device, selected from at least one of an online spectrophotometer, a multispectral camera, or an industrial camera calibrated with a standard color chart, is used to collect the colorimetric and density values ​​of printed materials. A paper property testing device for collecting at least one of the following: paper whiteness, moisture content, smoothness, and thickness; An ink characteristic detection device, used to collect at least one of ink viscosity, ink temperature and ink color density; Equipment status sensors are used to collect at least two of the following: ink supply, ink key opening, ink roller temperature, printing pressure, water supply, printing speed, and actual output of the actuator. Environmental sensors are used to collect workshop temperature and relative humidity.

3. The printing color deviation prediction and compensation method according to claim 1, characterized in that: The preprocessing described in step S2 includes: A linear interpolation method based on a unified time reference is used to perform time alignment on multimodal data with different sampling frequencies; Differentiated filtering strategies are employed to remove noise based on the noise characteristics of different modal data. A regression-based completion method based on multimodal association is used to complete missing values. When the missing rate of a certain modality exceeds a preset threshold, the data segment is marked as unusable. Multimodal data are uniformly mapped to a preset numerical range for normalization processing.

4. The printing color deviation prediction and compensation method according to claim 1, characterized in that: In step S2, the preprocessed features of each modality are first mapped by the corresponding linear projection layer to modal feature vectors of a preset dimension for unifying the dimension and subsequent attention weighting; the preset attention network outputs scalar attention scores for each modality, and the weight parameters of the attention network are predetermined and stored in a fixed manner through offline training; each attention score is converted into the weight of each modality by the softmax function, and the weighted modal feature vectors are concatenated in a preset order to form the fusion state vector, and a mapping table between the feature coordinates in the modal feature vector and the fusion state vector and the corresponding acquisition engineering variables or variable groups is established simultaneously.

5. The printing color deviation prediction and compensation method according to claim 4, characterized in that: Step S3, which involves constructing the color deviation cause-effect graph model, specifically includes: Based on the time series of variables after preprocessing of each collected engineering variable in the multimodal preprocessing data, and with reference to the mapping table, a set of candidate variables related to color deviation is determined. The set of candidate variables includes uncontrollable disturbance variables, compensation execution variables, printing process status variables, and color error variables. Based on historical operational data of candidate variable sets and safety perturbation response data of actuators, a directed acyclic graph structure is constructed using a data-driven structure search algorithm combined with scoring criteria, and the allowed directions of directed edges are limited by printing process topological constraints. For directed edges connected to the compensation execution variable, the local effect coefficient is determined based on the local response slope before and after the corresponding safety perturbation; for the other directed edges, the local effect coefficient is determined based on the partial derivative of the conditional expectation function of the variable and its parent node set. Using color error as the target variable, the directed paths pointing to the target variable are identified. The product of the local effect coefficients on each path is taken as the path influence degree. Based on the path influence degree, key factors are identified, and the color deviation cause analysis results, including a list of key factors, a ranking of contributions, and a description of the action path, are output.

6. The printing color deviation prediction and compensation method according to claim 5, characterized in that: The printing process topology constraints include: uncontrollable disturbance variable nodes are only allowed to point to printing process state variable nodes or color error variable nodes; compensation execution variable nodes are only allowed to point to printing process state variable nodes that can be physically adjusted by the corresponding actuator; the direction of the directed edges between printing process state variable nodes is limited according to the paper feeding direction, ink transfer order, or energy transfer order; in the color deviation time delay causal graph model, color error variable nodes are not used as parent nodes of compensation execution variable nodes.

7. The printing color deviation prediction and compensation method according to claim 5, characterized in that: Each directed edge is associated with a response delay parameter, which is determined by the cross-correlation or transfer entropy of the variable time series and verified by the safety perturbation response data of the corresponding actuator. When the recent multimodal data is determined to have changed significantly after distribution test, the graph structure is relearned in the state of stopping the automatic issuance of new compensation instructions or running in shadow model, and the current model is replaced after verification.

8. The printing color deviation prediction and compensation method according to claim 1, characterized in that: Step S4 specifically includes: Based on the color deviation cause analysis results, the deviation between the current color state and the target color standard is determined, and the deviation includes at least two signed color error components. Select one or more variables from the adjustable variables of the printing equipment that have an effective action path with at least one color error component and whose total path gain absolute value reaches the minimum controllable threshold as compensation execution variables; The local effect coefficients on each action path from each compensation execution variable to each color error component are multiplied together, and the gains of parallel paths connecting the same compensation execution variable and the same color error component are summed to form an actuator-color sensitivity matrix. Based on the predicted color error at the target observation time, the actuator-color sensitivity matrix, and the execution cost, the adjustment amount of each compensation execution variable is solved under the constraints of actuator amplitude, rate of change, and printing process coupling. The adjustment amounts of each compensation execution variable are integrated into a structured color compensation strategy, which includes a list of device parameters to be adjusted, the adjustment direction and magnitude of each parameter, the execution sequence and priority.

9. The printing color deviation prediction and compensation method according to claim 1, characterized in that: In step S5, the response delays on each action path are accumulated to obtain the path response delays. The path response delays of the same compensation execution variable are weighted according to the absolute value of the path gain to obtain the comprehensive response delay. Based on the target observation time, the compensation execution variable with a longer comprehensive response delay receives the control command first, and the compensation execution variable with a shorter comprehensive response delay receives the control command later, so that the main compensation effects of different actuators act on the printed matter together near the target observation time.

10. A printing color deviation prediction and compensation system, characterized in that: It includes a multimodal sensor array, an industrial computer or edge server, a printing equipment control interface, and an actuator connected to the printing equipment control interface; The industrial computer or edge server includes: The data acquisition module is used to acquire timestamped printed image color data, paper characteristic data, ink characteristic data, equipment operating parameter data, and environmental parameter data through the multimodal sensor group; The data preprocessing and fusion module is used to perform time alignment, noise filtering, missing value processing and normalization on multimodal data, and to perform weighted concatenation of features of each modality based on a preset attention network to generate a fusion state vector that preserves the physical mapping relationship of variables. The causal reasoning module is used to construct a color deviation delay causal graph model based on variable time series, fused state vector, printing process topology and actuator safety perturbation response data, determine local effect coefficients and response delay, and output key factors and their action paths. The compensation strategy generation module is used to form an actuator-color sensitivity matrix based on the local effect coefficients of each action path, and to solve the adjustment amount of the compensation execution variable under the coupling constraints of actuator amplitude, rate of change and printing process to generate a color compensation strategy. The compensation execution and verification module is used to output equipment operating parameter adjustment instructions to the actuator through the printing equipment control interface based on the comprehensive response delay, and to verify the compensation effect and trigger model updates or iterations based on the compensated printed image color data.

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