A multi-interval optimization control method for printing dry temperature

Abstract

The present application relates to a kind of multi-interval optimization control methods of printing dry temperature, to solve the problem that temperature control appears space-time coordination misalignment in dynamic operating condition in printing drying process, because of the difference of the inherent heat conduction path and energy storage characteristics (i.e. thermal inertia) of multiple physical sections, including: constructing thermal inertia fingerprint model library;Combining real-time running speed to identify operating condition and match target thermal inertia fingerprint model combination, generate nonlinear distribution matrix;Calculate the compensation amount containing amplitude adjustment and phase correction and superimposed with reference set flow to generate temperature set value;Through double-channel feedback, closed-loop regulation and residual monitoring are carried out.The method effectively solves the problem of temperature field coordination misalignment caused by inherent differences in thermal inertia of multiple sections, significantly improves the temperature field consistency and long-term operation stability of the system in dynamic operating condition.

Description

Technical Field

[0001] This invention relates to the field of temperature control technology for the drying process of printing equipment, and in particular to a multi-range optimized control method for printing drying temperature. Background Technology

[0002] Current printing equipment drying process temperature control technology is widely used in modern roll / flatbed gravure, flexographic, offset, and digital inkjet printing processes. Its basic goal is to achieve rapid curing of inks or coatings and stable finished product quality under different printing speeds, material properties, and environmental variables through segmented temperature zones and multi-stage drying. Currently, printing drying temperature control mostly adopts tuning strategies based on the speed-temperature mapping relationship, combined with closed-loop regulation algorithms, to achieve basic temperature management for each zone.

[0003] However, when the printing speed changes dynamically or the type of substrate is switched, the existing control strategy is difficult to effectively coordinate the different response times and energy requirements of each section due to the inherent thermal inertia differences. This can easily lead to improper heat distribution between sections and a lag in the dynamic following of the overall temperature field, affecting the uniformity of substrate surface drying.

[0004] In addition, after long-term operation of the drying equipment, factors such as aging of heating elements and changes in the condition of the air duct system can cause varying degrees of drift in the thermal efficiency of each section. Existing control schemes rely on fixed parameter operation, which makes it difficult to adaptively compensate for this slow change, thus posing a challenge to the inter-section coordination consistency under long-term operation. Summary of the Invention

[0005] This application provides a multi-zone optimization control method for printing drying temperature, which aims to solve the problem of spatiotemporal coordination inaccuracy in temperature control under dynamic conditions caused by the differences in the inherent heat conduction paths and energy storage characteristics (i.e., thermal inertia) of multiple physical zones during the printing drying process.

[0006] This application provides a multi-range optimization control method for printing drying temperature, specifically including: The temperature response curves of the substrate surface at the outlet, the temperature rise curve of the air duct, and the power input sequence of each physical section of the printing drying equipment under step temperature excitation are obtained. Combined with the substrate type and ink solid content parameters, a thermal inertia fingerprint model library is constructed.

[0007] Based on the thermal inertial fingerprint model library, the operating conditions of the printing equipment are identified by the real-time collected operating speed, and a current operating condition label including acceleration, constant speed, deceleration or transient change state is generated.

[0008] Using the current operating condition label as a retrieval index, the target thermal inertial fingerprint model combination with the highest fit with the response characteristics of each interval is matched from the thermal inertial fingerprint model library, and a nonlinear allocation matrix of collaborative weights for each interval is generated based on the printing speed change rate.

[0009] A baseline setting flow is generated based on the global velocity-temperature mapping relationship, and the interval-specific compensation amount, including amplitude adjustment and phase correction terms, is calculated by combining the target thermal inertial fingerprint model with the nonlinear allocation matrix to form a compensation correction flow.

[0010] The reference set flow and the compensation correction flow are superimposed to generate a sequence of temperature set values ​​for each interval to compensate for the heat conduction hysteresis effect.

[0011] Dual-channel feedback control is executed based on the temperature setpoint sequence of each interval. While the main channel performs closed-loop adjustment within the interval, the auxiliary channel calculates the residual sequence between the actual thermal response trajectory and the predicted trajectory of the corresponding thermal inertial fingerprint model.

[0012] If the residual sequence exceeds a preset threshold, an incremental neural network update mechanism is triggered to fine-tune the parameters of the target thermal inertial fingerprint model in the thermal inertial fingerprint model library online.

[0013] The multi-zone optimization control method for printing drying temperature provided in this application has the following beneficial effects: By acquiring response data under step excitation in each section and integrating printing material and ink parameters, a thermal inertial fingerprint model library characterizing the heat conduction and energy storage properties of each section is constructed. Based on this, dynamic operating conditions are identified and the optimal thermal inertial fingerprint model combination is matched, generating a weight matrix for each section according to the rate of change of velocity. Then, section-specific compensation amounts, including amplitude adjustment and phase correction, are calculated and superimposed with the baseline setpoint to generate a temperature setpoint that eliminates the heat conduction hysteresis effect. Finally, closed-loop regulation and residual monitoring are performed through dual-channel feedback. This method effectively solves the problem of spatiotemporal inaccuracy of the temperature field caused by inherent differences in thermal inertia across multiple sections, significantly improving the consistency of the temperature field and long-term operational stability of the system under dynamic conditions, thus helping to ensure printing quality. Attached Figure Description

[0014] Figure 1 This is the main flowchart of a multi-range optimization control method for printing drying temperature.

[0015] Figure 2 This is a sub-flowchart of a multi-range optimization control method for printing drying temperature.

[0016] Figure 3 This is a flowchart of the dynamic confidence threshold determination method for a multi-range optimization control method of printing drying temperature. Detailed Implementation

[0017] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0018] The following disclosure provides many different embodiments or examples for implementing different structures of the invention. To simplify the disclosure, specific examples of components and arrangements are described below. Of course, these are merely examples and are not intended to limit the invention. Furthermore, reference numerals and / or letters may be repeated in different examples; such repetition is for simplification and clarity and does not in itself indicate a relationship between the various embodiments and / or arrangements discussed.

[0019] like Figure 1 As shown, this application provides a multi-range optimization control method for printing drying temperature, specifically including: S1: Obtain the surface temperature response curve of the substrate at the outlet, the temperature rise curve of the air duct, and the power input sequence of each physical section of the printing drying equipment under step temperature excitation. Combine the substrate type and ink solid content parameters to construct a thermal inertial fingerprint model library characterizing the heat conduction path and energy storage characteristics of each section.

[0020] S2: Based on the thermal inertial fingerprint model library, the operating conditions of the printing equipment are identified by the real-time collected operating speed, and the current operating condition label is generated, which includes acceleration, constant speed, deceleration or transient change state.

[0021] S3: Using the current working condition label as the retrieval index, the target thermal inertial fingerprint model combination with the highest fit with the response characteristics of each interval is matched from the thermal inertial fingerprint model library, and a nonlinear allocation matrix of the collaborative weights of each interval is generated based on the printing speed change rate.

[0022] S4: Generate a baseline setting flow based on the global velocity-temperature mapping relationship, and use the target thermal inertial fingerprint model combination and nonlinear allocation matrix to calculate the interval-specific compensation amount including amplitude adjustment and phase correction terms, forming a compensation correction flow.

[0023] S5: Superimpose the reference set flow and the compensation correction flow to generate a sequence of temperature set values ​​for each interval to compensate for the heat conduction hysteresis effect.

[0024] S6: Based on the temperature setpoint sequence of each interval, dual-channel feedback control is executed. While the main channel performs closed-loop regulation within the interval, the auxiliary channel calculates the residual sequence between the actual thermal response trajectory and the corresponding thermal inertial fingerprint model predicted trajectory.

[0025] S7: Determine whether the residual sequence exceeds the preset threshold. If it does, trigger the incremental neural network update mechanism to fine-tune the parameters of the target thermal inertial fingerprint model in the thermal inertial fingerprint model library online.

[0026] like Figure 2 As shown, step S1: Obtain the outlet substrate surface temperature response curve, air duct temperature rise curve, and power input sequence of each physical section of the printing drying equipment under step temperature excitation. Combined with the substrate type and ink solid content parameters, construct a thermal inertial fingerprint model library characterizing the heat conduction path and energy storage characteristics of each section. Specifically, this includes: S1.1: Apply step temperature excitation signals independently to each physical section of the printing drying equipment, and simultaneously collect the surface temperature response curve of the substrate at the outlet, the temperature rise curve of the air duct, and the power input sequence to obtain an initial response dataset characterizing the original thermal dynamic behavior of each section.

[0027] Sub-step S1.1 aims to obtain raw thermal dynamic response data of the dry section through controlled excitation experiments, providing a basic dataset for constructing a thermal inertial fingerprint model.

[0028] Start the calibration mode of the printing drying equipment, isolate the physical drying section to be tested, and suspend the substrate conveying to eliminate the interference of material movement on the thermal field distribution, ensuring the static stability of the test environment.

[0029] A constant amplitude step temperature excitation signal is applied to the heating actuator in this section, and a preset threshold is set to increase the target temperature relative to the initial ambient temperature, thus forming a clear heat input boundary condition.

[0030] A high-precision data acquisition system is synchronously triggered to record the heating power input sequence in real time at a millisecond-level sampling frequency, capturing the instantaneous fluctuation characteristics in the process of electrical energy being converted into thermal energy.

[0031] By using a non-contact infrared temperature sensor array, the temperature change curve of the simulated substrate surface at the outlet of the drying section is continuously monitored and recorded to obtain thermal response data that directly reflects the drying effect.

[0032] Simultaneously, temperature rise curve data inside the air duct are collected, and the air temperature lag and attenuation characteristics in the hot air circulation system are recorded to supplement key dimension information characterizing convective heat transfer efficiency.

[0033] The power input sequence, surface temperature response curve, and duct temperature rise curve were strictly aligned on the time axis. Start-up transient noise and sensor drift error were eliminated, and an initial response dataset characterizing the original thermal dynamic behavior of this section was generated.

[0034] By independently applying step excitation and simultaneously acquiring data from multiple sources, the thermal behavior of the physical section is transformed into multi-dimensional time-series data containing power, surface temperature, and duct temperature. This achieves a complete digital mapping of the heat conduction path and energy storage characteristics of the drying section, laying a data foundation for the subsequent extraction of low-dimensional time-series feature vectors.

[0035] For example, in the second drying unit of a high-speed gravure printing machine, the step excitation temperature was set to jump from 60°C to 80°C. Data was continuously collected for 120 seconds at a sampling interval of 10ms. The heating power was recorded to linearly increase from 2kW to 5kW within 0-5 seconds and remain stable; the substrate surface temperature reached 70°C at 15 seconds and tended to a steady state of 79.5°C at 45 seconds; the duct temperature reached a steady state approximately 3 seconds later than the surface temperature. After aligning these three sets of time-series data, an initial response dataset containing 36,000 data points was formed, fully recording the thermal inertia performance under specific operating conditions within this range.

[0036] S1.2: Based on the initial response dataset and combined with the preset substrate type parameters and ink solid content parameters, perform multi-source data fusion processing to generate a composite thermal response feature vector containing working condition context information.

[0037] Receive the initial response dataset acquired in S1.1, including the surface temperature response curve of the printing substrate at the outlet, the temperature rise curve of the air duct, and the power input sequence. Read the preset printing material type parameters and ink solid content parameters as operating context constraints.

[0038] Timestamp alignment is performed on the multi-source time-series signals in the initial response dataset to eliminate phase deviations caused by differences in sensor sampling frequencies and to construct a multi-dimensional data matrix with a unified time reference.

[0039] The Z-Score normalization method is used to perform dimensionless processing on temperature, wind speed and power data, eliminating the interference of different physical dimensions on feature fusion weights and generating normalized dynamic response data streams.

[0040] By mapping the type of printing material to a discrete encoding vector and the solid content of ink to a continuous numerical scalar, a static working condition feature vector characterizing the thermal properties of the medium is constructed.

[0041] By using weighted tensor product operations, the normalized dynamic response data stream and the static operating condition feature vector are fused in a multi-dimensional space to generate a composite thermal response feature vector that contains coupled information of thermodynamic behavior and medium properties.

[0042] By using the multi-source data fusion processing method described above, the raw data collected in the previous step is transformed into a composite thermal response feature vector containing working condition context information, thereby achieving precise binding between thermal response characteristics and specific printing process conditions, and providing a high signal-to-noise ratio data foundation for subsequent low-dimensional feature extraction.

[0043] For example, in the third drying section of a high-speed rotary printing press, temperature response sequence, duct temperature rise sequence, and power sequence were collected with a sampling rate of 100Hz. The printing substrate was 80g / m² coated paper, coded as [0,1,0], and the ink solid content was 65%. The temperature data were Z-score normalized, with a mean of 45℃ and a standard deviation of 5℃. The static feature vector [0,1,0,0.65] was fused with the dynamic data stream using tensor product to generate a composite feature matrix of dimension N×4. This matrix fully preserves the thermal hysteresis information under abrupt velocity changes and the material's heat absorption characteristics, significantly improving the ability of the subsequent fingerprint model to characterize nonlinear heat load changes.

[0044] S1.3: The composite thermal response feature vector is analyzed using a low-dimensional time-series feature extraction algorithm to calculate the rise time, peak lag, steady-state deviation rate, and decay oscillation mode index, so as to output a low-dimensional time-series feature vector that characterizes the heat conduction path and energy storage characteristics of each section.

[0045] Receive the composite thermal response feature vector generated by S1.2, which includes operating context information. This vector integrates multi-dimensional time-series data of substrate surface temperature, air duct temperature rise, and power input.

[0046] The first derivative operation is performed on the temperature response curve in the composite thermal response feature vector to extract the slope change rate during the temperature rise phase. The time interval required from the excitation start point to reaching 95% of the steady-state value is calculated by integration and defined as the rise time index to quantify the thermal response speed of the segment.

[0047] Identify the time difference between the peak point of the temperature response curve and the application of the step excitation, calculate the peak hysteresis index, which is used to characterize the delay characteristics in the heat conduction path and reflect the inertial resistance of heat energy transfer from the heating source to the surface of the substrate.

[0048] Extract the last 10% of the temperature response curve after it enters steady state, calculate the absolute value of the deviation between its mean and the theoretical set temperature, and divide it by the set temperature to obtain the steady-state deviation rate, thus evaluating the thermal balance accuracy of the section under continuous heating.

[0049] A fast Fourier transform is performed on the decay phase of the temperature response curve after it exceeds the peak value to extract the dominant oscillation frequency and its corresponding damping ratio, construct a decay oscillation mode index, and characterize the dynamic oscillation characteristics generated by the interaction between thermal capacity and thermal resistance within the section.

[0050] By combining the above-mentioned rise time, peak lag, steady-state deviation rate and damped oscillation mode indicators, a low-dimensional time series feature vector is formed. This vector uniquely identifies the heat conduction path and energy storage characteristics of the drying section under a specific material-ink combination using four-dimensional spatial coordinates.

[0051] In this application, thermal inertia refers to the comprehensive characteristics of the temperature response in the time domain under step temperature excitation, which are caused by differences in physical structures such as the length of the heat conduction path, the size of the heat capacity, and the distribution of thermal resistance. It is quantitatively characterized by four low-dimensional time-series characteristic indicators: rise time, peak lag, steady-state deviation rate, and decaying oscillation mode.

[0052] By using a low-dimensional time-series feature extraction algorithm, the high-dimensional composite thermal response data from the previous step is transformed into a low-dimensional time-series feature vector with clear physical meaning, thereby realizing the digital fingerprint characterization of the thermal inertia of each section and providing a standardized benchmark for subsequent operating condition matching.

[0053] For example, for the first drying section of a printing unit, the collected composite thermal response feature vector, after processing, yielded a rise time of 12.5 seconds, a peak hysteresis of 3.2 seconds, a steady-state deviation rate of 0.8%, and a damping ratio of 0.65 for the damped oscillation mode. These values ​​were normalized to form a four-dimensional vector [0.45, 0.32, 0.08, 0.65]. This vector, serving as the thermal inertia fingerprint of this section under a specific combination of coated paper and UV ink, significantly distinguishes its response characteristics from those of other sections, ensuring the uniqueness and recognizability of fingerprints in the model library and effectively supporting subsequent precise decoupling control of nonlinear thermal load changes.

[0054] S1.4: Construct a thermal inertial fingerprint model that uniquely identifies the thermal response characteristics of a specific material-ink combination based on low-dimensional time-series feature vectors, and store the generated thermal inertial fingerprint model in the thermal inertial fingerprint model library to complete the construction of the thermal inertial fingerprint model library characterizing the thermal characteristics of each segment.

[0055] The system receives the low-dimensional time-series feature vector output from S1.3, which includes rise time, peak lag, steady-state deviation rate, and damped oscillation mode indices. A multi-dimensional index key-value structure is constructed, using the substrate material type code and ink solid content value as the primary key, and the physical segment identifier as the secondary key, establishing a mapping relationship between the feature vector and operating parameters. Euclidean distance clustering is used to calculate the centroids of multiple test feature vectors under the same material-ink combination, eliminating random noise interference and generating a standard thermal inertial fingerprint prototype. The storage data structure of the fingerprint model is defined, including the feature mean vector, covariance matrix, and confidence labels, ensuring the model's statistical representativeness. The generated standard thermal inertial fingerprint prototype is serialized and written to a thermal inertial fingerprint model library in non-volatile storage media, with a version-controlled index established. Through the above processing, discrete feature data is transformed into a structured, searchable thermal inertial fingerprint model library, achieving unique identification and persistent storage of the individual thermal response of each interval, providing a standardized data foundation for subsequent operating condition matching.

[0056] For example, test data was collected for the third drying section of a certain type of gravure printing press when the paper type was coated paper and the ink solid content was 45%. The extracted low-dimensional time-series feature vector is [2.5s, 0.8s, 1.2%, 0.05]. The system clustered the feature vectors of 10 repeated tests under this condition using "coated paper_45%" as the primary key and "Zone_3" as the secondary key, and calculated the mean vector [2.48s, 0.79s, 1.18%, 0.048] and covariance matrix. This standard fingerprint prototype was stored in the model library, generating a unique ID "FP_Zone3_Paper_Cu_Ink_45_v1". In subsequent operations, the system can quickly retrieve and call the thermal response characteristics under this specific working condition through this ID, significantly improving the accuracy and response speed of model matching.

[0057] Step S2: Based on the thermal inertial fingerprint model library, identify the operating condition of the printing equipment by analyzing the real-time collected operating speed data, and generate current operating condition tags that include acceleration, constant speed, deceleration, or transient change states. Specifically, this includes: S2.1: Perform sliding window difference operation on the real-time acquired printing equipment operating speed sequence to obtain a data stream representing the instantaneous dynamic changes in printing speed change rate, and perform secondary difference processing based on the printing speed change rate data stream to generate a second-order differential feature sequence of printing speed representing the acceleration change trend.

[0058] Substep S2.1 aims to extract differential features from the real-time printing speed sequence to quantify the trend of heat load changes under dynamic operating conditions. It acquires the raw data sequence of the printing equipment's operating speed within a high-frequency sampling period, which includes instantaneous noise caused by mechanical transmission fluctuations.

[0059] A sliding window difference operation is performed on the real-time acquired printing equipment operating speed sequence to calculate the speed difference between the current moment and the previous moment, and to obtain the printing speed change rate data stream; then, a second difference processing is performed on the printing speed change rate data stream to obtain the second-order differential feature sequence of printing speed.

[0060] An adaptive Kalman filter algorithm is introduced to denoise the second-order differential feature sequence, eliminate high-frequency mechanical vibration interference, and retain the low-frequency trend component that reflects the sudden changes in the actual working conditions.

[0061] The filtered rate of change of velocity is aligned with the second-order differential feature by timestamp to form a two-dimensional dynamic feature vector containing amplitude intensity and curvature of change.

[0062] Through the above differential operations and filtering, discrete velocity sampling points are transformed into continuous dynamic characteristic indicators that characterize the urgency of thermal inertial response, thus realizing a refined quantitative description of acceleration, deceleration and transient change conditions.

[0063] For example, the sampling frequency is set to 100Hz, and the sliding window length N is 10. When the printing speed linearly increases from 50m / min to 60m / min within 0.5 seconds, the calculated rate of change of speed v'(t) stabilizes at 20m / min / s, and the second-order differential feature v''(t) is close to 0, indicating a uniform acceleration condition. If the speed experiences a step fluctuation of 2m / min within 0.1 seconds, v'(t) shows a spike, and v''(t) increases significantly. After Kalman filtering, the abrupt change feature is preserved, accurately capturing the risk of transient thermal shock and providing high-precision input for subsequent condition label generation.

[0064] S2.2: Based on the printing speed change rate data stream and the second-order differential feature sequence of printing speed, a multi-dimensional working condition feature vector containing amplitude intensity and curvature information is constructed. The multi-dimensional working condition feature vector is then scaled using a pre-set normalization mapping function to output a standardized working condition feature vector that eliminates dimensional differences.

[0065] The received output data stream of printing speed change rate and the second-order differential feature sequence of printing speed are used as the basic input data for constructing a multi-dimensional working condition feature vector.

[0066] Extract the instantaneous absolute value of the printing speed change rate data stream to characterize the intensity level of the current printing process heat load change, and define it as the amplitude intensity component.

[0067] The local curvature index of the second-order differential characteristic sequence of printing speed is calculated by using the difference ratio of adjacent time windows to quantify the degree of speed change, which is defined as the changing curvature component.

[0068] The amplitude intensity component and the curvature variation component are vector-concatenated to construct the original multidimensional working condition feature vector containing dynamic intensity and dynamic trend information.

[0069] The preset normalization mapping function is invoked to perform scale standardization on the multidimensional working condition feature vector, and each component is linearly transformed to the dimensionless interval.

[0070] The calculated standardized amplitude intensity component and standardized curvature component are recombined to generate a standardized chemical condition feature vector that eliminates the influence of dimensions.

[0071] By using a normalized mapping process, the original multidimensional features from the previous step are transformed into dimensionless standard working condition feature vectors, thereby improving the accuracy and accelerating the convergence of subsequent working condition similarity calculations.

[0072] For example, the threshold for the printing speed change rate is set to 5 m / s², and the threshold for the second-order differential curvature is set to 2 m / s³. The current speed change rate is collected to be 3.5 m / s², and the second-order differential value is 1.2 m / s³. In historical calibration data, the speed change rate ranges from [0, 10] m / s², and the second-order differential value ranges from [0, 5] m / s³. The standardized amplitude intensity is calculated as (3.5-0) / (10-0) = 0.35, and the standardized curvature is (1.2-0) / (5-0) = 0.24. The generated standardized operating condition feature vector is [0.35, 0.24]. This vector eliminates dimensional differences and can be directly used for subsequent Euclidean distance calculations, significantly improving the response speed and matching accuracy of operating condition identification.

[0073] S2.3: Use the low-dimensional time-series feature vectors pre-stored in the thermal inertial fingerprint model library as the benchmark for judging operating conditions, calculate the Euclidean distance metric between the standardized operating condition feature vector and each low-dimensional time-series feature vector, and generate a set of operating condition similarity scores that characterize the degree of matching between the real-time operating state and the typical thermal response mode.

[0074] We call upon the pre-stored low-dimensional time-series feature vectors of each interval in the thermal inertial fingerprint model library and define them as the standard operating condition discrimination benchmark set. We extract the output standard operating condition feature vector, which includes the normalized printing speed change rate and second-order differential features. We construct a Euclidean distance metric algorithm to quantify the geometric difference between the real-time operating condition vector and the benchmark vector in the library.

[0075] The Euclidean distance between the real-time operating condition vector of the i-th drying section and the baseline vector of the j-th fingerprint model is calculated using the following formula: in, For the first Section and the The Euclidean distance of the model, For the feature vector dimension, The first real-time operating condition vector dimensional components, The fingerprint model baseline vector is the first Dimensional components.

[0076] The process iterates through all candidate models in the thermal inertial fingerprint model library, performing the aforementioned distance calculation for each model to generate a distance scalar sequence. The calculated Euclidean distance values ​​are then mapped to a working condition similarity score, with similarity set to be inversely proportional to distance; the smaller the distance, the higher the similarity. The calculation results for all dry sections are then summarized to form a set of working condition similarity scores characterizing the degree of matching between the real-time operating state and each typical thermal response mode.

[0077] By using Euclidean distance metric processing, the standard working condition feature vector from the previous step is transformed into a quantified set of working condition similarity scores, which enables accurate quantification of the matching degree between the current printing dynamic working condition and the historical thermal response pattern, providing a reliable data foundation for subsequent maximum likelihood estimation decisions.

[0078] For example, let the feature vector dimension n be 4, corresponding to the rate of change of velocity, acceleration, temperature response hysteresis, and steady-state deviation, respectively. The real-time acquired standard operating condition feature vector is [0.8, 0.5, 0.2, 0.1]. The baseline vector of a certain acceleration state fingerprint model in the library is [0.75, 0.45, 0.25, 0.15]. Substitute these values ​​into the formula to calculate the sum of squares of the differences in each dimension: (0.8 - 0.75) 2 +(0.5-0.45) 2 +(0.2-0.25) 2 +(0.1-0.15) 2 =0.0025+0.0025+0.0025+0.0025=0.01. Taking the square root of this sum gives an Euclidean distance of 0.1. Converting this distance to a similarity score S=1 / (1+d), the score is 0.909. Comparing this to the distances of other state models, such as the uniform velocity state (distance 0.5, score 0.667), the acceleration state model has the highest similarity in the final generated similarity score set, accurately reflecting the current high-speed acceleration condition.

[0079] S2.4: Based on the set of working condition similarity scores, the maximum likelihood estimation decision algorithm is executed to select the working condition similarity score with the highest matching degree, and generate the current working condition label containing the identifiers of acceleration state, constant speed state, deceleration state or transient change state, so as to complete the accurate identification of the dynamic working conditions of the printing drying process.

[0080] Receive the generated set of operating condition similarity scores, which contains the Euclidean distance metric between the real-time standardized operating condition feature vector and the low-dimensional time-series feature vectors of each typical operating condition in the thermal inertial fingerprint model library.

[0081] A working condition discrimination function based on maximum likelihood estimation is constructed, which maps the inverse of the Euclidean distance to the probability of occurrence of each candidate working condition. The smaller the distance, the higher the probability, thereby quantifying the confidence that the current running data belongs to a specific dynamic mode.

[0082] Normalization is performed on the calculated conditional probabilities of each working condition to ensure that the sum of the probabilities of all candidate states is 1, thus eliminating the influence of dimensional differences on the decision boundary.

[0083] By introducing Bayesian decision rules, we compare the posterior probability values ​​of each working condition after normalization and identify the working condition category with the highest probability value as the optimal matching result.

[0084] For four preset state labels—acceleration, constant speed, deceleration, and transient change—probability threshold criteria are set for each. When the maximum probability value exceeds the preset threshold, the corresponding working condition label is locked.

[0085] If the maximum probability value is lower than the confidence threshold, it is determined that the current state is in transition. The operating condition label of the previous cycle is retained and marked as a state to be confirmed, so as to avoid frequent changes in control commands due to noise interference.

[0086] The output includes current operating condition labels indicating acceleration, constant speed, deceleration, or transient change, enabling accurate identification of the dynamic operating conditions during the printing and drying process.

[0087] By using the maximum likelihood estimation decision algorithm, the similarity score from the previous step is transformed into a statistically significant probability distribution of the operating conditions, thus achieving robust classification and accurate identification of complex thermal load conditions caused by nonlinear velocity changes.

[0088] For example, the regularization constant ε is set to 0.001, and the confidence threshold is 0.85. When the real-time velocity change rate is 5 m / s², and the second derivative is 0.2 m / s³, the calculated distance to the acceleration state fingerprint is 0.3, and the distance to the uniform state fingerprint is 1.5. The calculated likelihood probability of the acceleration state is approximately 11.1, and the likelihood probability of the uniform state is approximately 0.44. After normalization, the posterior probability of the acceleration state is significantly higher than that of other states and exceeds the 0.85 threshold. The system decisively outputs the "acceleration state" label, effectively avoiding misjudgments caused by velocity fluctuations and ensuring the timeliness of subsequent control strategy switching.

[0089] Step S3: Using the current operating condition label as a retrieval index, match the target thermal inertial fingerprint model combination with the highest fit to the response characteristics of each interval from the thermal inertial fingerprint model library, and generate a nonlinear allocation matrix of collaborative weights for each interval based on the printing speed change rate. Specifically, this includes: S3.1: Based on the generated current operating condition label, perform a partition search operation on the thermal inertial fingerprint model library to obtain the corresponding set of candidate thermal inertial fingerprint models, thereby narrowing the model matching range and establishing the initial search space.

[0090] Receive the generated current operating condition label containing the identifiers of acceleration, constant speed, deceleration, or transient change state, and input it as the main index key value into the retrieval interface of the thermal inertial fingerprint model library.

[0091] The current working condition label's state semantics are parsed and mapped to a predefined working condition partition index table in the model library, locking in a specific sub-library region that matches the current dynamic features.

[0092] Within the locked sub-database area, extract the metadata of candidate thermal inertial fingerprint models for all associated dry sections, including model ID, applicable speed range, and basic thermal response parameters.

[0093] Perform an integrity check on the extracted candidate model set to ensure that there is at least one corresponding candidate model instance for each physically dry section, in order to construct a complete initial search space.

[0094] By using a partitioned retrieval process, the massive global model library data stream is transformed into a small set of candidate thermal inertial fingerprint models limited to the current operating context, thereby optimizing retrieval efficiency and establishing the initial search boundary for subsequent refined matching.

[0095] For example, when the current operating condition label is identified as "acceleration state," the system accesses the partition marked "Dynamic-Accel" in the model library. This partition pre-stores 20 candidate fingerprint models for the first to fourth drying sections when the rate of change of velocity is greater than 0.5 m / s². The system extracts the metadata of these 20 models, including the rise time threshold range (e.g., 0.8 s–1.2 s) and peak hysteresis coefficient for each model. After verification, 5 candidate models for each section are loaded into memory, forming a candidate set containing 20 objects, providing an accurate data foundation for the multidimensional similarity measurement of S3.2, and significantly reducing the computation time of full library traversal.

[0096] S3.2: Utilize the real-time collected printing speed change rate and its second-order differential features to perform multi-dimensional similarity measurement calculation on the low-dimensional time-series feature vectors in the candidate thermal inertial fingerprint model set, so as to output the fit score sequence between each interval and the candidate thermal inertial fingerprint model, and quantify the degree of matching between the model and the current working condition.

[0097] Extract the printing speed change rate and the second derivative of the printing speed within the current control cycle to construct a real-time operating condition feature vector characterizing the dynamic intensity of the transient operating condition.

[0098] The rise time, peak lag, steady-state deviation rate, and decaying oscillation mode index of each model are extracted from the candidate thermal inertial fingerprint model set and recombined into a standardized low-dimensional time series feature vector.

[0099] The weighted Euclidean distance algorithm is used to calculate the spatial distance between the real-time operating condition feature vector and the low-dimensional time series feature vector of each candidate model, thereby quantifying the degree of difference between the two in thermal response characteristics.

[0100] The following formula is used to calculate the fit score between the i-th dry segment and the j-th candidate fingerprint model: in, Rate the compatibility. For the first Real-time operating condition feature vector of the section For the first Feature vectors of candidate fingerprint models To adjust the sensitivity coefficient.

[0101] An exponential mapping transformation is performed on the calculated raw distance values ​​to convert the distance metric into a probabilistic fit score in the range of 0 to 1, with a higher score for smaller distances.

[0102] Sort all candidate model fit scores by numerical value to generate a fit score sequence that includes the matching priority of each model.

[0103] By using weighted Euclidean distance calculation and exponential mapping transformation, the candidate model set from the previous step is transformed into a quantified fit score sequence data, thereby achieving a precise quantitative evaluation of the expected technical effect of matching the optimal thermal response model for each interval under the current velocity state.

[0104] For example, in the third dry section, the real-time velocity change rate is 2.5 m / s², and the second derivative is 0.8 m / s³. In the candidate library, model A has feature vectors of [2.4, 0.7, 0.05, 0.1], and model B has [3.0, 1.2, 0.1, 0.2]. Setting σ=0.5, the distance norm for model A is calculated to be 0.15, and for model B, it is 0.65. Substituting these values ​​into the formula, the fit score for model A is 0.956, and for model B, it is 0.548. The system determines model A to be a high-fit model, significantly improving the accuracy of subsequent weight allocation.

[0105] S3.3: Perform maximum likelihood estimation screening based on the fit score sequence to extract the candidate thermal inertial fingerprint model with the highest fit from the candidate thermal inertial fingerprint model set, so as to construct a target thermal inertial fingerprint model combination that represents the optimal response characteristics of each interval under the current velocity state.

[0106] The system receives the fit score sequence between each interval and the candidate thermal inertial fingerprint model output by S3.2. This sequence quantifies the degree of matching between the current real-time operating condition and the features of each pre-stored model.

[0107] Using the maximum likelihood estimation principle, log-likelihood values ​​are calculated for the candidate model set of each dry section. The specific candidate model that makes the likelihood function reach its maximum value is identified and marked as the optimal response model under the current operating condition, so as to construct a target thermal inertial fingerprint model combination that characterizes the optimal response characteristics of each section under the current speed state.

[0108] Iterate through the log-likelihood values ​​of all candidate models, execute the extreme value search algorithm, and identify the specific candidate model index that makes the likelihood function reach the global maximum.

[0109] The candidate thermal inertial fingerprint model corresponding to the highest likelihood value is marked as the optimal response model under the current operating conditions, ensuring that the selected model is statistically closest to the thermal dynamic characteristics of the actual physical system.

[0110] The above screening process is repeated for each interval in turn. The optimal response models selected from each interval are arranged in physical order and combined to form a target thermal inertial fingerprint model combination.

[0111] By using maximum likelihood estimation for screening, the fit score sequence from the previous step is transformed into a combination of target thermal inertial fingerprint models with statistical optimality, thereby accurately constructing the optimal response characteristics of each interval under the current velocity state and providing a high-confidence model foundation for subsequent nonlinear weight allocation.

[0112] For example, for the third drying section of the printing press, S3.2 outputs five candidate model matching scores of 0.85, 0.92, 0.78, 0.88, and 0.95. The mean score μ is set to 0.876, and the standard deviation σ is set to 0.06. The log-likelihood value of each score is calculated, and the score of 0.95 has the highest log-likelihood value, which is determined to be the best match. The system selects the thermal inertial fingerprint model with index 5 as the target model for this section. The same operation is performed on other sections, ultimately generating a combination containing the target models for the five sections, significantly improving the accuracy and robustness of model matching.

[0113] S3.4: Based on the target thermal inertial fingerprint model combination and the magnitude of the real-time printing speed change rate, perform nonlinear mapping function operation to generate an initial collaborative weight vector characterizing the difference in thermal response priority between each interval.

[0114] Obtain the target thermal inertial fingerprint model combination output from step S3.3, and extract the low-dimensional time-series feature vectors corresponding to each interval, including rise time, peak hysteresis and steady-state deviation rate parameters.

[0115] Read the real-time printing speed change rate data stream, calculate its absolute value to characterize the dynamic intensity of the current working condition, and use it as the master control variable for nonlinear mapping.

[0116] A nonlinear weight allocation model based on the hyperbolic tangent function is constructed to map the rate of change of velocity to an adjustment coefficient for interval response priority.

[0117] The initial collaborative weights of the i-th drying section are calculated using the following formula: in, For the first Initial collaborative weights for the interval, As a sensitivity adjustment factor, For real-time printing speed change rate, The threshold for velocity change, These are the basic weighting coefficients determined based on the peak lag time in thermal inertial fingerprints; the shorter the peak lag time, the lower the weighting coefficients. The higher the value, the more it reflects the priority compensation requirement of the front-end fast response section when there are sudden speed changes.

[0118] For the fast-response segment at the front end, a higher base weight coefficient α is set based on its short rise time. i This ensures that energy compensation is prioritized during rapid velocity changes.

[0119] For the long-latency section at the back end, a lower base weighting coefficient α is set based on its large peak lag characteristic. i This helps to suppress the risk of overshoot caused by excessive thermal inertia.

[0120] The calculated weight values ​​for each interval are combined into a vector to form the initial collaborative weight vector.

[0121] By using a nonlinear mapping process, the target thermal inertial fingerprint model and real-time velocity change rate from the previous step are transformed into an initial collaborative weight vector, thereby realizing the dynamic and differentiated allocation of thermal response priorities for each interval and providing a weight basis for the subsequent generation of temperature setpoints to eliminate hysteresis.

[0122] For example, the sensitivity adjustment factor k is set to 0.5, and the speed change threshold v0 is set to 10 m / min. When the real-time printing speed change rate is 20 m / min, the basic weighting coefficient α1 for the front-end section with a rise time of 5 s is set to 0.8; and the basic weighting coefficient α2 for the back-end section with a peak lag of 30 s is set to 0.3. Substituting into the formula, the initial collaborative weight w1 for the front-end section is approximately 0.62, and the initial collaborative weight w2 for the back-end section is approximately 0.23. This weight allocation significantly improves the response priority of the front-end section under accelerated conditions, effectively suppresses the thermal hysteresis effect of the back-end section, and ensures the dynamic stability of the drying temperature.

[0123] S3.5: Perform normalization constraints and dynamic smoothing filtering on the initial collaborative weight vector to eliminate weight jump interference and generate the final nonlinear allocation matrix.

[0124] Obtain the generated initial collaborative weight vector, which contains the original thermal response priority values ​​calculated for each interval based on the current operating condition label and the rate of change of velocity.

[0125] The initial collaborative weight vector is normalized using the L1 norm to ensure that the sum of weights in all intervals is always equal to 1. Then, the exponentially weighted moving average algorithm is used for time-domain smoothing filtering to suppress weight jumps and generate the final nonlinear allocation matrix.

[0126] A dynamic smoothing filter is constructed, and the normalized weight sequence is filtered in the time domain using an exponentially weighted moving average algorithm to suppress weight jumps caused by high-frequency noise.

[0127] Set a smoothing coefficient alpha, and dynamically adjust the alpha value according to the amplitude of the second-order differential characteristic of the printing speed. Decrease alpha when the acceleration changes drastically to enhance response sensitivity, and increase alpha when the operation is stable to improve stability.

[0128] Using the final nonlinear allocation matrix of the previous control cycle as the historical state input, and combining the current normalized weights and dynamic smoothing coefficients, the smoothing weight value at the current moment is iteratively calculated.

[0129] Boundary constraint verification is performed on the smoothed weight vector, forcibly truncating weight components that exceed the preset threshold range to allowable extreme values ​​to prevent overload or underload in a single interval.

[0130] By using normalization constraints and dynamic smoothing filtering, the initial cooperative weights from the previous step are transformed into a final nonlinear allocation matrix that has temporal continuity and physical feasibility, thereby achieving a balance between robustness and smoothness in multi-interval cooperative control.

[0131] For example, for a four-zone drying device, the initial weight vector is [0.4, 0.3, 0.2, 0.1]. After L1 normalization, the original proportions are maintained. Let the smoothing coefficient alpha be 0.8, and the previous period matrix be [0.35, 0.35, 0.2, 0.1]. The current smoothing weights are calculated to be [0.39, 0.31, 0.2, 0.1]. After boundary checks confirm no exceedances, the final matrix is ​​output. This processing effectively eliminates weight oscillations caused by velocity perturbations, reduces the rate of change of the temperature setpoint, and significantly improves the stability of the drying process.

[0132] Step S4: Generate a baseline setting flow based on the global velocity-temperature mapping relationship, and calculate the interval-specific compensation amount, including amplitude adjustment and phase correction terms, using the target thermal inertial fingerprint model combination and nonlinear allocation matrix to form a compensation correction flow. Specifically, this includes: S4.1: Perform a global speed-temperature mapping function operation on the real-time acquired printing speed data to generate a reference set flow for each interval that characterizes the basic process requirements.

[0133] The real-time acquisition of printing equipment operating speed data sequence is used as the input variable of the global speed-temperature mapping function to characterize the linear velocity state of the current substrate as it passes through the drying section.

[0134] The printing speed data sequence is subjected to sliding window mean filtering to remove instantaneous high-frequency noise caused by encoder pulse jitter or mechanical transmission backlash, and the smoothed effective printing speed value is output.

[0135] The global speed-temperature mapping lookup table, which is pre-stored in the controller memory, is invoked. This lookup table is derived from historical process big data statistics and establishes a non-linear mapping relationship between different printing speed ranges and the basic temperature requirements of the corresponding drying sections.

[0136] Based on the smoothed effective printing speed value, piecewise linear interpolation is performed in the pre-stored global speed-temperature mapping lookup table to determine the reference temperature target value for each interval corresponding to the current speed point.

[0137] The calculated target values ​​of the reference temperature for each interval are arranged in segment order to generate a reference set flow data sequence for each interval that characterizes the basic process requirements.

[0138] By performing global speed-temperature mapping function calculations and interpolation, the real-time changing printing speed is converted into the basic temperature setpoint for each interval, forming a reference setpoint stream. This provides a stable reference for subsequent dynamic compensation, ensuring the matching of drying temperature and printing speed under steady-state conditions.

[0139] For example, the printing speed is 60 m / min, and the speed nodes in the lookup table are 50 m / min and 70 m / min, corresponding to reference temperatures of 120°C and 130°C for the first drying section, respectively. Interpolation calculation: T b,1 =120+((60-50) / (70-50))*(130-120)=125℃. Similarly, calculate the reference temperature for other sections to generate the reference set flow [125,135,140]℃. This sequence accurately reflects the basic heat demand at the current speed and eliminates the set value jump caused by speed fluctuations.

[0140] S4.2: Utilize the low-dimensional temporal feature vector in the target thermal inertial fingerprint model combination, combined with the second-order differential feature of the current rate of change of velocity, to execute the thermal hysteresis phase prediction algorithm to calculate the phase correction term sequence used to offset the thermal conduction delay.

[0141] The peak lag time parameter and damped oscillation mode coefficients are extracted from the target thermal inertial fingerprint model to construct a basic delay vector characterizing the thermal response hysteresis characteristics of each section. The second-order differential eigenvalue of the real-time printing speed change rate is obtained; this value reflects the severity of the acceleration change and serves as the main control variable for dynamic phase correction. Based on the approximate solution of the heat conduction-diffusion equation, a nonlinear mapping relationship is established between the phase correction quantity and the second-order derivative of the velocity and the thermal inertial parameters. The phase correction term for the i-th drying section is calculated using the following formula: in, For the first Phase correction time of the section This represents the peak lag time in the fingerprint model. This is the second derivative of the rate of change of printing speed. and is the fitting constant.

[0142] The calculated original phase correction terms are sign-determined: a positive second derivative of velocity is marked as a phase advance, and a negative derivative as a phase lag compensation. A smoothing factor is introduced to weight the phase correction terms of adjacent control cycles, suppressing phase jumps caused by sensor noise. The processed phase correction values ​​are converted into discrete-time step indices, forming a sequence of phase correction terms that corresponds one-to-one with each interval.

[0143] By using the aforementioned thermal hysteresis phase prediction algorithm, static thermal inertia parameters are transformed into dynamic phase compensation commands, enabling accurate prediction and cancellation of heat conduction delay, and significantly improving the real-time response accuracy of temperature control.

[0144] S4.3: Based on the target thermal inertial fingerprint model combination and nonlinear allocation matrix, perform weighted gain calculation to calculate the amplitude adjustment sequence to adapt to the current nonlinear thermal load abrupt change.

[0145] The low-dimensional temporal feature vector and nonlinear allocation matrix of the target thermal inertial fingerprint model combination are obtained as the input benchmark for amplitude adjustment calculation.

[0146] We analyze the steady-state gain coefficient and dynamic time constant of each interval in the target fingerprint model to represent the thermal response sensitivity, and construct an interval thermal response sensitivity mapping table.

[0147] Extract the collaborative weight components of each interval in the nonlinear allocation matrix. These weight components represent the priority of each interval's contribution to the change in total heat load under the current printing speed change rate.

[0148] Based on the product relationship between the steady-state gain coefficient and the cooperative weight component, the initial amplitude adjustment factor for each interval is calculated to quantify the linear influence of velocity mutation on the temperature setting of a specific interval.

[0149] The second-order differential characteristic of printing speed is introduced as a nonlinear correction term, and the initial amplitude adjustment factor is dynamically weighted by an exponential decay function to compensate for the nonlinear hysteresis effect in the heat conduction process.

[0150] The amplitude adjustment for the i-th drying section is calculated using the following formula: in, Let be the steady-state gain coefficient for the i-th interval. The collaborative weights in the nonlinear allocation matrix, The rate of change of printing speed. The second-order differential characteristic of printing speed, The dynamic time constant, This serves as the normalized time reference.

[0151] The calculated amplitude adjustment sequence is subjected to amplitude limiting protection to ensure that the adjustment amplitude does not exceed the maximum power response threshold of the heating element of the equipment, thus preventing overshoot and damage to the substrate.

[0152] By using the weighted gain calculation method described above, the target fingerprint model and weight matrix of the previous step are transformed into an amplitude adjustment sequence that adapts to the current nonlinear heat load mutation, thereby achieving fine dynamic compensation for the temperature setpoint of each interval and significantly improving the temperature control robustness of the system under high-speed variable speed conditions.

[0153] For example, for the third drying section, its steady-state gain coefficient Ki is 1.2℃ / (m / min), and the co-weight wi is 0.35. When the printing speed change rate v' is 5m / min², the second-order differential characteristic v'' is 2m / min³, the dynamic time constant τ is 10s, and the normalized time base Tc is 50s, substituting into the formula, the exponential term exp(-10*2 / 50)=exp(-0.4)≈0.67. The amplitude adjustment Δ3=1.2*0.35*5*0.67≈1.41℃. This adjustment is superimposed on the reference set flow, effectively offsetting the insufficient heat caused by the speed acceleration, reducing the temperature fluctuation range of the exit substrate to within ±0.5℃, and significantly improving the consistency of drying quality.

[0154] S4.4: Perform a vector synthesis operation on the phase correction term sequence and the amplitude adjustment quantity sequence to generate interval-specific compensation quantities containing complete dynamic compensation information, forming an independent compensation correction flow.

[0155] Obtain the phase correction term sequence generated in S4.2 and the amplitude adjustment quantity sequence generated in S4.3 as the basic data input for constructing the interval-specific compensation quantity.

[0156] A two-dimensional complex domain mapping space is established, the amplitude adjustment is defined as a real part vector, the phase correction term is converted into an imaginary part vector, and a complex compensation vector characterizing the dynamic compensation characteristics is constructed.

[0157] A vector synthesis operation is performed on the phase correction term sequence and the amplitude adjustment quantity sequence to generate a localized compensation quantity for each interval containing complete dynamic compensation information, forming an independent compensation correction flow.

[0158] The synthesized complex compensation vector is normalized to eliminate the weight imbalance caused by the difference in dimensions, and to ensure that the compensation amount is within the physically executable range.

[0159] A dynamic smoothing filter is introduced to perform time-domain filtering on the normalized compensation vector, suppressing high-frequency noise interference and generating a stable interval-specific compensation quantity sequence.

[0160] By using vector synthesis and filtering, discrete amplitude and phase parameters are transformed into compensation correction streams containing complete dynamic compensation information, thereby achieving accurate cancellation and phase advance compensation for nonlinear heat load abrupt changes in each interval.

[0161] Step S5: Superimpose the reference setpoint flow and the compensated correction flow to generate a sequence of temperature setpoint values ​​for each interval to compensate for the heat conduction hysteresis effect. Specifically, this includes: S5.1: Perform data alignment processing on the generated interval-specific compensation quantities containing amplitude adjustment sequence and phase correction term sequence to obtain compensation correction stream data frames that are strictly synchronized with the current control cycle timestamp.

[0162] Obtain the dedicated compensation data stream for each interval generated by S4. This data stream contains the amplitude adjustment sequence and the phase correction term sequence, and its sampling timestamp is generated based on the microsecond-level control cycle under high-speed dynamic conditions.

[0163] Establish a time alignment window based on the start time of the current control cycle, read the original time label of each data point in the compensation correction stream, and calculate the time deviation value between it and the standard control cycle grid point.

[0164] Linear interpolation or zero-order hold algorithm is used to resample the compensation data with slight time jitter, and the non-uniformly distributed time series is mapped to a unified standard time axis to ensure that the compensation data of all segments are strictly synchronized in the time domain.

[0165] The amplitude adjustment and phase correction terms after resampling are vector-encapsulated to construct a standardized compensation correction stream data frame containing timestamp, segment ID, amplitude component and phase component, thereby eliminating data misalignment caused by sensor acquisition delay or communication jitter.

[0166] By using the above data alignment processing method, the asynchronous compensation amount generated in the previous step is transformed into a compensation correction stream data frame that is strictly synchronized with the current control cycle timestamp, thereby achieving accurate alignment of multi-source dynamic compensation signals in the time domain and providing a data basis without phase error for subsequent superposition operations with the reference setting stream.

[0167] For example, the original sampling times of the compensation correction stream are t=10.002ms and 10.005ms, corresponding to amplitude adjustments of +1.5℃ and +1.8℃. The standard control period is set to an integer multiple of 10ms. The data at t=10.002ms is aligned to the t=10.000ms grid using linear interpolation, and the aligned amplitude is calculated to be +1.48℃. The final output is a synchronized data frame with timestamps strictly at 10.000ms, 20.000ms..., eliminating millisecond-level timing deviations and ensuring the accuracy of the superposition operation.

[0168] S5.2: Based on real-time printing speed data, the reference setting streams for each interval are generated by the global speed-temperature mapping function. The reference setting streams are then resampled using a time series interpolation algorithm to obtain a synchronous reference setting stream with the same sampling frequency and phase reference as the compensation correction stream data frame.

[0169] The generated reference set flow data sequence for each interval is obtained. This sequence is generated based on the global velocity-temperature mapping relationship and represents the basic process temperature requirements. Its sampling frequency is usually lower than that of the compensation correction flow, resulting in asynchrony between the two in the time domain.

[0170] The timestamp alignment analysis method is used to identify the timing deviation between the timestamp of each sampling point in the baseline set stream data sequence and the sampling time of the compensation correction stream data frame in the current control cycle. A mapping relationship containing the original time point set of the baseline stream and the target synchronization time point set is constructed to determine the boundary conditions of the resampling grid and the distribution of interpolation nodes.

[0171] Furthermore, a continuous and differentiable temperature change curve function is constructed by nonlinearly fitting the original reference set flow using a cubic spline interpolation algorithm, so as to preserve the smoothness of temperature change and avoid high-frequency noise caused by linear interpolation.

[0172] Using a continuous temperature change curve function, interpolated temperature values ​​are calculated at the target time node of the resampling grid, generating a synchronous reference setting stream with the same sampling frequency and phase reference. This synchronous reference setting stream explicitly contains the base temperature target value that strictly corresponds to each compensation correction stream data frame.

[0173] By using the time series interpolation method described above, the asynchronous or non-uniformly sampled reference setpoint stream is transformed into a data frame that is strictly synchronized with the compensation correction stream, thereby achieving precise alignment of multi-source control signals in the time domain. This provides a data basis for subsequent superposition operations to eliminate phase errors and ensures that the final generated temperature setpoint sequence can accurately reflect the superposition result of basic process requirements and dynamic compensation effects.

[0174] For example, the baseline set stream sampling rate is 10Hz, and the compensation correction stream sampling rate is 50Hz. Three data points (0,100), (0.1,102), and (0.2,105) within the interval t=0.0s to t=0.2s in the baseline stream are selected, corresponding to the target base temperatures of 100℃, 102℃, and 105℃, respectively. A cubic spline interpolation function S(t) is constructed, satisfying S(0)=100, S(0.1)=102, S(0.2)=105 and the natural boundary conditions S''(0)=0, S''(0.2)=0. After solving for the polynomial coefficients of each interval, the values ​​of S(t) are calculated at the target resampling points t=0.02s, 0.04s, ..., 0.20s. For example, at t=0.02s, S(0.02)=100.4℃ is calculated; at t=0.04s, S(0.04)=100.8℃ is calculated. This generates a synchronous reference setpoint stream sequence [100.4,100.8,...,105] containing 10 data points. Each value in this sequence is the base temperature target value and completely coincides with the compensation correction stream on the time axis, eliminating the control lag error caused by sampling rate differences and significantly improving the dynamic response accuracy of temperature control.

[0175] S5.3: Perform point-by-point algebraic superposition on the base temperature target value in the synchronous reference setting stream and the amplitude adjustment sequence in the compensation correction stream data frame to generate an amplitude-corrected temperature sequence that eliminates steady-state deviation and adapts to the current nonlinear heat load abrupt change.

[0176] Acquire the synchronization reference setpoint stream data frame after S5.2 resampling processing. This data frame contains a sequence of base temperature target values ​​that are strictly time-aligned with the compensation correction streams of each interval. Extract the base temperature target value of the i-th drying section in the synchronization reference setpoint stream during the current control period k.

[0177] From the compensation correction stream data frame generated by S5.1, the amplitude adjustment amount corresponding to the i-th drying section in the current control period k is parsed out. This adjustment amount is obtained by weighted solution of nonlinear allocation matrix and thermal inertial fingerprint model.

[0178] The target temperature value in the synchronous reference setting stream is superimposed point by point with the amplitude adjustment amount in the compensation correction stream to generate an amplitude-corrected temperature sequence.

[0179] Iterate through all drying zone indices i and all sampling points within the current control cycle, repeating the above superposition operation. Arrange the calculated amplitude-corrected temperature values ​​for each zone in chronological order to construct an amplitude-corrected temperature sequence. This sequence eliminates steady-state temperature deviations caused by sudden rate changes, preserving the temperature reference required for the basic process.

[0180] By using a point-by-point algebraic superposition, the synchronous reference setting flow and dynamic amplitude compensation amount from the previous step are transformed into an amplitude-corrected temperature sequence, thus achieving the initial elimination of steady-state deviations caused by sudden changes in nonlinear thermal load and providing an accurate amplitude basis for subsequent phase correction.

[0181] For example, in the third drying section, at t=0.1s, the target base temperature in the synchronous reference setpoint is 120.5℃. At this time, the printing speed increases sharply, and the amplitude adjustment calculated by S4.3 is +3.2℃. The calculated amplitude-corrected temperature is 120.5 + 3.2 = 123.7℃. If the speed decreases sharply, the amplitude adjustment is -2.1℃, and the amplitude-corrected temperature is 120.5 - 2.1 = 118.4℃. The system performs this calculation on all six drying sections, generating a temperature vector containing six amplitude correction elements [102.1, 115.3, 123.7, 130.2, 125.8, 110.5]. This vector accurately reflects the instantaneous heat compensation required by each section under the current speed condition, significantly improving the sensitivity of the temperature setpoint to dynamic conditions.

[0182] S5.4: Perform time-domain translation transformation based on the amplitude-corrected temperature sequence and the phase correction term sequence in the compensation correction stream data frame to generate a phase-corrected temperature sequence that includes phase advance compensation to offset the control lag caused by heat conduction delay.

[0183] Obtain the generated amplitude-corrected temperature sequence and the phase correction term sequence in the compensation correction stream data frame. This phase correction term sequence represents the time advance required for each interval to compensate for the thermal conduction delay.

[0184] The phase offset time value corresponding to each sampling point in the phase correction term sequence is analyzed. Combined with the sampling interval of the current control cycle, the translation step size of each sampling point in the time domain is calculated, and the mapping index relationship of the time domain translation transformation is determined.

[0185] For the temperature sequence after amplitude correction, a time-domain translation operation is performed. For translation requirements with non-integer step sizes, a linear interpolation method is used to reconstruct the translated temperature values ​​to ensure that the temperature setpoint has a leading displacement on the time axis that meets the phase correction requirements.

[0186] A time-domain translation transformation model is constructed to map the original timestamp t to the leading timestamp t', where t' = t + Δφ, and Δφ is the phase correction term. Based on the leading time determined by the phase correction term, a time-domain translation transformation is performed on the amplitude-corrected temperature sequence to generate a phase-corrected temperature sequence containing phase advance compensation.

[0187] For the missing boundary data generated during the translation process, zero-order hold or mirror extension strategies are used to fill the gaps, ensuring the data integrity and continuity of the temperature sequence after phase correction and avoiding breakpoints in the control commands.

[0188] By using time-domain translation transformation, the amplitude-corrected temperature sequence is transformed into a phase-corrected temperature sequence that includes phase advance compensation, thereby achieving active cancellation of heat conduction delay and significantly improving the dynamic response speed and tracking accuracy of temperature control to sudden velocity changes.

[0189] For example, the temperature sequence after amplitude correction in a certain dry section is 120℃ at t=1.0s and 122℃ at t=1.1s. If the calculated phase correction Δφ=0.05s, then the temperature value at t=1.05s needs to be obtained as the output for the current time. Linear interpolation is used for calculation: T p =120+(122-120)*(0.05 / 0.1)=121℃. This 121℃ is sent as the final set value at t=1.0s, causing the heater to start earlier, effectively compensating for the thermal lag of about 0.05s, reducing the overshoot of the substrate surface temperature under sudden speed change conditions, and shortening the response time.

[0190] S5.5: Perform boundary constraint verification and smoothing filtering on the phase-corrected temperature sequence to output the final temperature setpoint sequence for each interval that eliminates heat conduction delay and adapts to rapid velocity changes, and send it to the execution layer controller.

[0191] Obtain the generated phase-corrected temperature sequence. Although the sequence already includes amplitude and phase compensation, the values ​​may exceed the physical limits of the device due to computational noise or extreme operating conditions.

[0192] Construct a set of temperature safety boundary constraints for each interval, including minimum ignition temperature, maximum tolerance temperature, and maximum temperature rise rate limit, to form a multi-dimensional feasible domain space.

[0193] Boundary truncation is performed on each data point in the phase-corrected temperature sequence, forcibly raising values ​​below the minimum ignition temperature to the lower limit and forcibly compressing values ​​above the maximum tolerance temperature to the upper limit, ensuring that the instructions are within the hardware safety range.

[0194] For the temperature sequence after boundary truncation, a finite impulse response filter is used to perform smoothing filtering to generate a continuous and stable temperature setpoint trajectory.

[0195] The smoothed final temperature setpoint sequence is encapsulated into a standard communication protocol data packet and sent in real time to the execution layer controllers of each zone via the industrial bus.

[0196] By performing boundary constraint verification and smoothing filtering, the temperature sequence after phase correction in the previous step is transformed into a final temperature setpoint sequence that conforms to hardware safety specifications and is free from high-frequency jitter, thereby achieving a balance between the safety, stability, and real-time performance of control commands.

[0197] For example, the safe temperature boundary for a certain drying section is set as [80℃, 220℃], with a maximum temperature rise rate of 5℃ / s. An instantaneous value of 225℃ appears in the phase-corrected sequence, which is then truncated to 220℃. An FIR filter with a window width M=2 is used to smooth the truncated sequence [218, 220, 219, 217]. The filtered value at the center point of 220℃ is calculated to be (218+220+219+217+216) / 5=218℃. This process eliminates the risk of exceeding the 225℃ limit and numerical jumps, outputting a smooth final setpoint of 218℃ to the PLC, ensuring smooth heater power adjustment and avoiding grid impact and material thermal damage.

[0198] Step S6: Execute dual-channel feedback control based on the temperature setpoint sequence for each interval. While performing closed-loop regulation within the interval in the main channel, the residual sequence between the actual thermal response trajectory and the corresponding thermal inertial fingerprint model predicted trajectory is calculated in the auxiliary channel. Specifically, this includes: S6.1: Obtain the generated temperature setpoint sequence for each interval and the real-time measured temperature data for each interval, and input both into the main channel proportional-integral-derivative controller for deviation calculation processing to generate the interval closed-loop control command sequence for driving the heating actuator.

[0199] Obtain the temperature setpoint sequence for each interval output from step S5. This sequence already includes phase advance compensation and amplitude adjustment information, and serves as the target reference value for the main channel control. Simultaneously collect the measured temperature data of the substrate surface at the exit of each interval, and obtain the real-time temperature feedback signal through a high-precision thermocouple sensor at a sampling frequency consistent with the control cycle.

[0200] The final temperature setpoint sequence and the measured temperature data are timestamped to ensure that they correspond strictly in the time domain, eliminating timing misalignment caused by data transmission delay, and constructing the basic dataset for calculating the temperature deviation of the current control cycle.

[0201] Based on the aligned data, point-by-point subtraction is performed to calculate the instantaneous deviation between the set temperature and the measured temperature, generating an original deviation sequence that characterizes the degree of deviation from the current thermal state. This sequence reflects the current steady-state error and dynamic response lag of the system.

[0202] The original deviation sequence is input to the main channel proportional-integral-derivative (PID) controller, where the proportional term is used to quickly respond to the current deviation, the integral term is used to eliminate the accumulated steady-state error, and the derivative term is used to predict the deviation change trend to suppress overshoot. After being solved by the proportional term, integral term, and derivative term in sequence, the heating power command is output.

[0203] The calculated heating power command sequence is subjected to amplitude limiting processing to constrain it within the safe operating range of the heating actuator, preventing equipment overload due to excessive commands or response failure due to insufficient commands, and generating the final closed-loop regulation command sequence within the range.

[0204] Through the above PID calculation and limiting processing, the deviation between the temperature setpoint and the measured value is converted into an executable heating power command, realizing rapid and accurate closed-loop regulation of the temperature in each zone, and ensuring the thermal stability of the drying process.

[0205] S6.2: Drive the drying equipment to operate based on the closed-loop control command sequence within the interval, synchronously collect the actual surface temperature response data of the printed material at the outlet of each interval, and integrate the actual surface temperature response data of the printed material into the actual thermal response trajectory that characterizes the current system's true thermal state.

[0206] The system receives a sequence of closed-loop control commands generated by the main channel within each zone. This sequence includes the power duty cycle or voltage control signals of the heating actuators in each zone, which serve as direct inputs to drive the drying equipment.

[0207] Based on the adjustment command sequence, control commands are sent to the solid-state relays or frequency converters in each zone via the industrial bus protocol, driving the infrared heating tubes or hot air circulating fans to output heat energy according to the set power, so that the printing substrate undergoes a preset heat exchange process during the transmission.

[0208] A high-precision non-contact infrared temperature sensor array is deployed at the exit of each section to collect the surface temperature data of the substrate in real time at a sampling frequency synchronized with the control cycle, thereby obtaining a sequence of original temperature measurement values ​​that reflect the actual thermal state.

[0209] The original temperature measurement sequence is subjected to spatiotemporal alignment processing. Combined with the real-time linear velocity data fed back by the printing speed sensor, the temperature sampling points in the time domain are mapped to the position coordinates of the drying section in the spatial domain, eliminating the position deviation caused by the fluctuation of the conveyor belt speed.

[0210] A sliding window midpoint filtering algorithm is used to suppress noise in the mapped temperature data, eliminating abnormal jump points caused by paper shaking or ambient light interference, and retaining trend data that represent the true heat distribution.

[0211] The filtered temperature data are integrated into a continuous actual thermal response trajectory vector in the order of timestamps. This vector fully records the actual temperature evolution of the substrate as it passes through each interval within the current control cycle.

[0212] Through the above data acquisition and preprocessing process, discrete sensor readings are transformed into actual thermal response trajectories with spatiotemporal consistency, providing high-fidelity benchmark data for residual calculation of the predicted trajectory in the subsequent auxiliary channel and thermal inertial fingerprint model, thus realizing accurate reproduction of the system's true thermal state.

[0213] For example, in the third drying section, the received closed-loop control command is a 65% power duty cycle. An infrared temperature sensor collects data at a frequency of 100Hz, obtaining 10 raw temperature points within a 0.1-second window: [145.2, 145.5, 148.9, 145.3, 145.1, 145.4, 145.2, 145.3, 145.5, 145.1]℃. The temperature at 148.9℃ is identified as abnormal noise. After median filtering, the effective data sequence is smoothed to [145.2, 145.3, 145.3, 145.3, 145.2]℃. Combined with the current printing speed of 2m / s, this sequence is mapped to a temperature distribution trajectory within a 0.2-meter radius of the exit. The final output actual thermal response trajectory vector accurately reflects the steady-state thermal output characteristics of this section at 65% power, eliminating instantaneous interference and ensuring the accuracy of subsequent residual calculations.

[0214] S6.3: Call the matching target thermal inertial fingerprint model, input the current printing speed change rate and power input sequence into the target thermal inertial fingerprint model to perform forward inference calculation, so as to generate the corresponding thermal inertial fingerprint model prediction trajectory that characterizes the ideal thermal dynamic behavior.

[0215] The target thermal inertial fingerprint model determined in step S3 is invoked. This model contains low-dimensional time-series feature vectors that characterize the heat conduction path and energy storage characteristics of a specific dry section.

[0216] The printing speed change rate data and the power input sequence of the heating actuator within the current control cycle are acquired and used as dynamic excitation inputs for the model's forward inference. The printing speed change rate is mapped to a heat load disturbance factor to quantify the nonlinear effect of wind speed changes on the convective heat transfer coefficient.

[0217] A heat source excitation function is constructed using the power input sequence to characterize the energy injection intensity of the heater into the air medium. Based on the rise time and peak hysteresis parameters in the target thermal inertial fingerprint model, a discrete state-space equation is established to describe the dynamic evolution of the temperature response.

[0218] The Runge-Kutta numerical integration method is used to solve the state equations, and the theoretical temperature response value at the next time step is calculated iteratively. Damping corrections are applied to the calculation results using damped oscillation mode indices to suppress high-frequency noise interference. A thermal inertial fingerprint model prediction trajectory sequence containing timestamps, predicted temperature values, and confidence intervals is generated.

[0219] Through the aforementioned forward extrapolation calculations, real-time operating data is transformed into a predicted trajectory characterizing ideal thermal dynamic behavior, providing a benchmark for subsequent residual calculations and enabling accurate prediction of nonlinear heat load changes.

[0220] For example, the target thermal inertial fingerprint model includes a rise time of 0.5 s, a peak lag of 1.2 s, a steady-state deviation rate of 2%, and a decay coefficient of 0.8. The current printing speed change rate is 5 m / s², and the power input is 5 kW. The speed change rate is mapped to a thermal load disturbance factor of 1.2, and the power input is normalized to 0.8. Substituting these values ​​into the discrete state-space equations, a sampling step size of 0.02 s is set. The Runge-Kutta method is used for iterative calculation to obtain the predicted temperature sequence for the next 1 s. At t=0.2 s, the predicted temperature is 102.5℃; at t=0.4 s, the predicted temperature is 104.8℃. A decay coefficient of 0.8 is applied to correct the oscillation components, eliminating high-frequency fluctuations. The generated predicted trajectory is smooth and conforms to the laws of physical thermal inertia, significantly reducing the deviation from the actual measured value and effectively improving the accuracy of the auxiliary channel residual calculation.

[0221] S6.4: In the auxiliary channel, point-by-point differential alignment processing is performed on the actual thermal response trajectory and the corresponding thermal inertial fingerprint model predicted trajectory. The numerical difference between the two in the time domain is calculated to generate an initial residual data stream that quantifies the degree of model mismatch.

[0222] The actual thermal response trajectory data synchronized and aligned in the auxiliary channel and the predicted trajectory data generated by the target thermal inertial fingerprint model are obtained. Both have the same timestamp sequence and sampling frequency.

[0223] A point-by-point subtraction operation is performed between the temperature values ​​in the actual thermal response trajectory and the temperature values ​​at the corresponding timestamps in the predicted trajectory to generate an initial residual data stream.

[0224] Iterate through all sampling points within the current control cycle to generate a complete initial residual data stream containing positive and negative deviation information.

[0225] The initial residual data stream is subjected to sign-preserving processing to retain the directional characteristics of the bias in order to distinguish between overheated and underheated states.

[0226] By using a point-by-point differential alignment process, the dual-trajectory data from the previous step is transformed into an initial residual data stream that quantifies the degree of model mismatch, thereby achieving an accurate characterization of the deviation of thermal dynamic behavior in each interval.

[0227] S6.5: Based on the sliding window filtering algorithm, noise suppression and temporal smoothing are performed on the initial residual data stream, and effective deviation features are extracted to output the residual sequence for subsequent threshold judgment and model update.

[0228] The initial residual data stream generated by the auxiliary channel calculation is obtained. This data stream contains the point-by-point difference values ​​in the time domain between the actual thermal response trajectory and the fingerprint model predicted trajectory, which are mixed with high-frequency noise from the sensor and transient interference signals.

[0229] A fixed-length sliding time window is constructed, with a window width of N sampling periods and a step size of 1 sampling period. The initial residual data stream is divided into several overlapping subsequence segments to establish the basic unit for local time series analysis.

[0230] Median filtering is performed on the residual subsequence within each sliding window to remove outlier extreme points caused by electromagnetic interference or sensor jitter, while retaining the median value that reflects the true thermal deviation trend of the system, thus achieving the first level of impulse noise suppression.

[0231] The weighted moving average algorithm is used to smooth the denoised residual sequence. Based on the Gaussian distribution function, weight coefficients that decay with time distance are generated. Differentiated weights are assigned to each residual point within the window, and the smoothed residual value is output.

[0232] Extract the first-order difference features of the smoothed residual sequence, calculate the rate of change of residual values ​​at adjacent time points, identify the abrupt changes and continuous drift trends of the residual signal, and distinguish between occasional disturbances and systematic model mismatch.

[0233] The extracted effective deviation features are truncated by thresholding, and small fluctuations below the noise threshold are set to zero, retaining only the deviation components with significant physical meaning, thus forming a sparse effective residual sequence.

[0234] By using sliding window filtering and feature extraction, the noisy initial residual data stream from the previous step is transformed into an effective residual sequence with high signal-to-noise ratio that characterizes the degree of mismatch in the real model, thereby improving the accuracy and stability of the subsequent model calibration trigger criteria.

[0235] For example, the sliding window width N is set to 20 sampling points, the sampling frequency is 50Hz, and the window duration is 0.4s. The Gaussian weight standard deviation σ is set to 3. Random high-frequency noise with an amplitude of ±0.5℃ in the initial residual sequence is suppressed to within ±0.05℃ after median filtering. After weighted moving average smoothing, the standard deviation of the residual sequence is reduced from 0.12℃ to 0.03℃. After extracting the first-order difference features, a positive drift trend of 0.2℃ / s lasting for more than 3 cycles is identified and determined to be a valid bias. The final output valid residual sequence clearly reflects the prediction lag of the thermal inertial fingerprint model caused by dust accumulation on the filter, providing a clean error feedback signal for the model update in step S7.

[0236] Step S7: Determine whether the residual sequence exceeds a preset threshold. If it does, trigger the incremental neural network update mechanism to fine-tune the parameters of the corresponding target thermal inertial fingerprint model in the thermal inertial fingerprint model library online. Specifically, this includes: S7.1: Obtain the residual sequence and calculate the root mean square error of the residual sequence based on the sliding window statistical algorithm to generate a residual energy index that characterizes the fitting accuracy of the current model.

[0237] The residual sequence output from the auxiliary channel, after being processed by a sliding window filter, is obtained. This sequence represents the temporal deviation between the actual thermal response trajectory and the trajectory predicted by the thermal inertial fingerprint model within the current control cycle. A time window slicing operation is performed on the residual sequence, and a sliding window of fixed length is set to extract the set of continuous residual data points within the window to construct a sample set for local error analysis.

[0238] Based on the local error analysis sample set, the root mean square error algorithm is used to calculate the quantitative index of residual energy. Specifically, the square of each residual data point within the window is calculated, all squared values ​​are summed and divided by the total number of sample points, and then the square root of the quotient is taken to generate a scalar form of residual energy value.

[0239] Through the above statistical calculations, the discrete residual sequence in the time domain is transformed into a single energy index characterizing the model fitting accuracy, realizing a quantitative assessment of the degree of mismatch of the thermal inertial fingerprint model under the current operating conditions, and providing an accurate basis for subsequent online calibration.

[0240] For example, the sliding window length N is set to 50 sampling points, and the sampling frequency is 10Hz, covering 5 seconds of historical data. During a printing speed change from 60m / min to 80m / min, the maximum deviation of the residual sequence within the window is 2.5℃. The sum of squares is calculated to be 312.5, divided by 50 to get 6.25, and the square root yields a residual energy index E of 2.5. This index is significantly higher than the baseline threshold of 0.5 under static conditions, accurately reflecting the model mismatch caused by the speed change, triggering the subsequent incremental neural network update mechanism, and ensuring the adaptive adjustment of the control strategy.

[0241] S7.2: Perform a comparison and judgment process based on the residual energy index and the preset dynamic confidence threshold. If the residual energy index exceeds the dynamic confidence threshold, a model mismatch trigger signal is generated to determine the start of the online calibration process for the target thermal inertial fingerprint model.

[0242] like Figure 3 As shown, the dynamic confidence threshold determination process in this step specifically includes: obtaining the residual energy index E and the real-time velocity change rate, calculating the dynamic confidence threshold, comparing E with the dynamic confidence threshold, and executing the model confidence maintenance or model mismatch trigger branch according to the comparison result.

[0243] Specifically, the residual energy index generated by the calculation is obtained, which quantifies the degree of fitting deviation between the current thermal inertial fingerprint model's predicted trajectory and the actual thermal response trajectory. A dynamic confidence threshold benchmark is set, which is preset based on the thermal sensitivity level of the printing material and the historical stability data of the equipment, and serves as an initial reference standard for judging whether the model is mismatched.

[0244] The absolute value of the printing speed change rate is introduced as a dynamic adjustment factor. An adaptive increment proportional to the speed change rate is superimposed on the benchmark threshold to generate a dynamic confidence threshold.

[0245] The residual energy index calculated in real time is compared with the dynamic confidence threshold. If the residual energy index is less than or equal to the dynamic confidence threshold, the model is determined to be in the confidence range, the current thermal inertial fingerprint model parameters are kept unchanged, and the monitoring process of the next control cycle continues.

[0246] If the residual energy index exceeds the dynamic confidence threshold, the current model is deemed unable to accurately characterize the system's thermal dynamics, and a high-level model mismatch trigger signal is generated. This trigger signal carries the current dry section identifier and timestamp, serving as the sole instruction to activate the subsequent incremental neural network update mechanism.

[0247] By using dynamic threshold comparison and judgment processing, the residual energy index is transformed into a clear Boolean logic signal of the model state, which realizes the accurate capture of the online calibration timing of the thermal inertial fingerprint model, avoids false triggering or missed triggering caused by fixed thresholds, and significantly improves the robustness and response efficiency of the adaptive calibration system.

[0248] For example, during the transient process of accelerating the printing speed from 50 m / min to 80 m / min, the preset reference threshold is 0.5℃, and the sensitivity coefficient is set to 0.02 s. When the detected rate of change of speed dv / dt is 15 m / min / s, the calculated dynamic confidence threshold is 0.8℃. If the residual energy index obtained by the sliding window statistics is 0.95℃ at this time, since 0.95℃ is greater than 0.8℃, the system immediately generates a model mismatch trigger signal and initiates the online calibration process for the thermal inertial fingerprint model of the third drying section; if the residual energy index is 0.7℃, the model is deemed valid, and no update is triggered, thereby reducing unnecessary computational overhead while ensuring control accuracy.

[0249] S7.3: In response to the model mismatch trigger signal, a local weight update network is constructed using the incremental backpropagation algorithm. The residual sequence is used as the error feedback input, and the low-dimensional temporal feature vector of the current target thermal inertial fingerprint model is used as the reference input to calculate the parameter correction gradient characterizing the drift of the heat conduction path.

[0250] In response to the model mismatch trigger signal, an incremental backpropagation algorithm is initiated to construct a local weight update network. The low-dimensional temporal feature vector of the current target thermal inertial fingerprint model is used as the baseline input layer data and mapped to the hidden layer nodes. The residual sequence output from the auxiliary channel is used as the error feedback signal and input to the output layer for bias quantization.

[0251] The partial derivatives of the loss function with respect to the network weights are calculated using the chain rule, and the initial gradient is smoothed by incorporating a momentum term to generate a cumulative corrected gradient. This cumulative corrected gradient characterizes the parameter shift in the heat conduction path caused by equipment aging or operational drift.

[0252] The accumulated correction gradient is distributed layer by layer to the connection weight matrix between the input layer and the hidden layer through backpropagation. An incremental update operation is performed on the weight matrix to generate a new set of weight parameters that reflects the current true thermal dynamic characteristics.

[0253] By using incremental backpropagation and momentum acceleration processing, the residual sequence from the previous step is transformed into a parameter correction gradient characterizing the drift of the heat conduction path, thereby achieving online adaptive calibration of the thermal inertial fingerprint model.

[0254] For example, setting an adaptive learning rate The root mean square error (RMSE) of the residual sequence is 0.01, and the momentum coefficient is 0.9. When the RMS error of the residual sequence exceeds the threshold of 0.5℃, a low-dimensional temporal feature vector [12.5, 3.2, 0.8] is extracted as input. The predicted value is calculated through forward propagation, and the residual is 0.6℃ when compared with the measured value. The partial derivative of the loss function with respect to the weights is calculated using the chain rule, and the cumulative correction gradient vector [0.02, -0.01, 0.03] is obtained by combining the momentum term. This gradient is applied to update the weight matrix, which significantly reduces the deviation between the model's predicted trajectory and the actual trajectory in the next control cycle, effectively compensating for the thermal response hysteresis caused by the decrease in heating tube efficiency.

[0255] S7.4: Based on the parameter correction gradient, perform iterative update operations on the parameters of the target thermal inertial fingerprint model stored in the thermal inertial fingerprint model library to generate an updated thermal inertial fingerprint model containing the latest thermal dynamic characteristics, thereby completing the adaptive calibration of the ability to adapt to nonlinear thermal load abrupt changes.

[0256] The calculated parameter correction gradient vector is received. This vector represents the sensitive direction and adjustment magnitude of each low-dimensional temporal feature parameter in the thermal inertial fingerprint model relative to the current residual error.

[0257] An incremental update operator is constructed, which performs element-wise multiplication of the parameter correction gradient with the preset learning rate coefficient to generate local incremental corrections for key fingerprint parameters such as rise time, peak lag, and steady-state deviation rate.

[0258] Read the original parameter baseline values ​​of the target thermal inertial fingerprint model currently matched from the thermal inertial fingerprint model library to ensure that the update operation is based on the latest stable state rather than historical outdated data.

[0259] The generated local incremental correction is vector-added with the original parameter baseline value to obtain the preliminarily updated thermal inertial fingerprint parameter set, realizing the step-by-step migration of model parameters along the error descent direction.

[0260] A momentum damping mechanism is introduced to apply an exponentially weighted moving average filter to the initially updated parameter set, suppressing the violent oscillations of parameters caused by instantaneous noise interference and enhancing the smoothness and stability of model updates.

[0261] Perform physical constraint boundary checks on the final updated parameters to ensure that the rise time is positive and the steady-state deviation rate is within a reasonable range, and eliminate abnormal parameter values ​​that violate thermodynamic physical laws.

[0262] The updated parameters, after passing the verification, are overwritten to the corresponding target model storage address in the thermal inertial fingerprint model library to complete the iterative update of the model version.

[0263] In the next control cycle, the updated target thermal inertial fingerprint model is called to replace the original model for model matching in S3 and forward inference prediction in S6, so as to realize the online evolution and continuous adaptation of the thermal inertial fingerprint model.

[0264] By using incremental gradient updates and momentum damping, the parameter correction gradient from the previous step is transformed into an updated thermal inertial fingerprint model with the latest thermal dynamic characteristics, thereby achieving adaptive calibration to adapt to sudden changes in nonlinear thermal loads.

[0265] For example, in the third drying section of a high-speed printing press, the initial thermal inertial fingerprint model has a rise time parameter of 12.5 s and a peak lag parameter of 4.2 s. When the printing speed suddenly increases from 80 m / min to 120 m / min, the auxiliary channel detects an excessive residual energy index, and the calculated correction gradient for the rise time is -0.8 s, and the correction gradient for the peak lag is -0.3 s. The adaptive learning rate is set to 0.1, and the momentum damping coefficient is 0.9. The calculated rise time increment is -0.08 s, and the peak lag increment is -0.03 s. After the initial update, the rise time is 12.42 s, and the peak lag is 4.17 s. After momentum smoothing, the final updated parameters are 12.43 s and 4.18 s, respectively. This calibration process significantly reduces the deviation between the model's predicted trajectory and the actual temperature response, significantly reduces the temperature control overshoot after a sudden speed change, and significantly improves the response speed.

[0266] For those skilled in the art, various other corresponding changes and modifications can be made based on the technical solutions and concepts described above, and all such changes and modifications should fall within the protection scope of the claims of this invention.

[0267] Unless otherwise defined, the technical or scientific terms used herein shall have the ordinary meaning as understood by one of ordinary skill in the art to which this application pertains. The terms “first,” “second,” “third,” and similar terms used in this patent application specification and claims do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Similarly, the terms “an” or “a” and similar terms do not indicate a quantity limitation, but rather indicate the presence of at least one. The terms “comprising” or “including” and similar terms mean that the element or object preceding “comprising” or “including” encompasses the element or object listed following “comprising” or “including” and its equivalents, and do not exclude other elements or objects. The “multiple” mentioned in the embodiments of this application refers to two or more. A and / or B indicate three possibilities: A; B; and A and B.

[0268] The above description is merely an exemplary embodiment of this application, but the scope of protection of this application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in this application, and such modifications or substitutions should all be covered within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A multi-interval optimization control method of printing dry temperature, characterized by, include: The temperature response curves of the substrate surface at the outlet, the temperature rise curve of the air duct, and the power input sequence of each physical section of the printing drying equipment under step temperature excitation are obtained. Combined with the substrate type and ink solid content parameters, a thermal inertia fingerprint model library is constructed. Based on the thermal inertial fingerprint model library, the operating conditions of the printing equipment are identified by the real-time collected operating speed, and a current operating condition label including acceleration, constant speed, deceleration or transient change state is generated. Using the current working condition label as a retrieval index, the target thermal inertial fingerprint model combination with the highest fit with the response characteristics of each interval is matched from the thermal inertial fingerprint model library, and a nonlinear allocation matrix of collaborative weights for each interval is generated based on the printing speed change rate. A baseline setting flow is generated based on the global velocity-temperature mapping relationship, and the interval-specific compensation amount, including amplitude adjustment and phase correction terms, is calculated by combining the target thermal inertial fingerprint model with the nonlinear allocation matrix to form a compensation correction flow. The reference set flow and the compensation correction flow are superimposed to generate a sequence of temperature set values ​​for each interval to compensate for the heat conduction hysteresis effect. Dual-channel feedback control is executed based on the temperature setpoint sequence of each interval. While the main channel performs closed-loop adjustment within the interval, the auxiliary channel calculates the residual sequence between the actual thermal response trajectory and the predicted trajectory of the corresponding thermal inertial fingerprint model.

2. The multi-interval optimization control method of printing drying temperature according to claim 1, characterized in that, After obtaining the residual sequence through calculation, the method further includes: If the residual sequence exceeds a preset threshold, an incremental neural network update mechanism is triggered to fine-tune the parameters of the target thermal inertial fingerprint model in the thermal inertial fingerprint model library online.

3. The multi-interval optimization control method of printing drying temperature according to claim 1, characterized in that, The acquisition of the outlet substrate surface temperature response curve, air duct temperature rise curve, and power input sequence of each physical section of the printing drying equipment under step temperature excitation, combined with the substrate type and ink solid content parameters, to construct a thermal inertia fingerprint model library, specifically including: Step temperature excitation signals are applied independently to each physical section of the printing drying equipment, and the surface temperature response curve of the substrate at the outlet, the temperature rise curve of the air duct, and the power input sequence are collected simultaneously to obtain the initial response dataset. Based on the initial response dataset and combined with the preset printing material type parameters and ink solid content parameters, multi-source data fusion processing is performed to generate a composite thermal response feature vector. The composite thermal response feature vector is analyzed using a low-dimensional time series feature extraction algorithm to calculate rise time, peak lag, steady-state deviation rate and damped oscillation mode index, and output a low-dimensional time series feature vector. A thermal inertial fingerprint model is constructed based on the low-dimensional temporal feature vector, and the generated thermal inertial fingerprint model is stored in the thermal inertial fingerprint model library.

4. The multi-interval optimization control method of printing drying temperature according to claim 1, characterized in that, The aforementioned method of generating a baseline setting flow based on the global velocity-temperature mapping relationship, and using the target thermal inertial fingerprint model combination and the nonlinear allocation matrix to calculate the interval-specific compensation amount including amplitude adjustment and phase correction terms, to form a compensation correction flow, specifically includes: A global speed-temperature mapping function is performed on the real-time acquired printing speed data to generate a reference set flow for each interval that characterizes the basic process requirements. Using the low-dimensional temporal feature vector in the target thermal inertial fingerprint model combination, combined with the second-order differential feature of the current rate of change of velocity, a thermal hysteresis phase prediction algorithm is executed to calculate the phase correction term sequence used to offset the thermal conduction delay. Based on the target thermal inertial fingerprint model combination and the nonlinear allocation matrix, a weighted gain calculation process is performed to calculate the amplitude adjustment sequence to adapt to the current nonlinear thermal load abrupt change. A vector synthesis operation is performed on the phase correction term sequence and the amplitude adjustment quantity sequence to generate a range-specific compensation quantity containing complete dynamic compensation information, forming an independent compensation correction flow.

5. The multi-range optimized control method for printing drying temperature according to claim 1, characterized in that, The process of identifying the operating status of the printing equipment by collecting real-time data on its operating speed specifically includes: The speed change rate is obtained by performing a sliding window difference on the operating speed of the printing equipment, and then the second-order differential feature of the speed is obtained by performing a second difference. Based on this, a multi-dimensional operating condition feature vector is constructed and normalized. The Euclidean distance between the multi-dimensional operating condition feature vector and each low-dimensional time-series feature vector in the thermal inertial fingerprint model library is calculated to generate an operating condition similarity score. The current operating condition label is output by maximum likelihood estimation.

6. The multi-range optimized control method for printing drying temperature according to claim 1, characterized in that, The step of matching the target thermal inertial fingerprint model combination that best matches the response characteristics of each interval from the thermal inertial fingerprint model library specifically includes: Based on the current operating condition label, the thermal inertial fingerprint model library is partitioned and searched. The fit score is calculated based on the printing speed change rate and the second-order differential feature of the speed. The target thermal inertial fingerprint model combination for each interval is obtained by maximum likelihood estimation.

7. The multi-range optimization control method for printing drying temperature according to claim 1, characterized in that, The step of superimposing the reference setpoint flow and the compensation correction flow to generate a sequence of temperature setpoint values ​​for each interval to compensate for the heat conduction hysteresis effect specifically includes: Data alignment is performed on the compensation correction stream, the reference setting stream is resampled to obtain the synchronous reference setting stream, the synchronous reference setting stream and the compensation correction stream are superimposed point by point and then phase correction is performed by time domain translation, and then the temperature setting value sequence of each interval is output after boundary constraint and smoothing filtering.

8. The multi-range optimized control method for printing drying temperature according to claim 1, characterized in that, The execution of dual-channel feedback control and calculation of the residual sequence specifically includes: In the main channel, the temperature setpoint sequence of each interval and the real-time measured temperature data of each interval are input into the PID controller for deviation calculation, and a closed-loop control command is generated to drive the drying equipment to operate. In the auxiliary channel, the actual thermal response trajectory is acquired, and the printing speed change rate and the power input sequence are input into the target thermal inertial fingerprint model for forward extrapolation to generate a predicted trajectory. The actual thermal response trajectory and the predicted trajectory are differentially analyzed point by point and filtered before the residual sequence is output.

9. The multi-range optimized control method for printing drying temperature according to claim 1, characterized in that, The nonlinear allocation matrix for generating collaborative weights for each interval based on the printing speed change rate specifically includes: Based on the target thermal inertial fingerprint model combination and the amplitude of the printing speed change rate, a nonlinear mapping is performed to generate an initial collaborative weight vector. Normalization constraints and dynamic smoothing filtering are then applied to the initial collaborative weight vector to generate the nonlinear allocation matrix.

10. The multi-range optimization control method for printing drying temperature according to claim 2, characterized in that, The online fine-tuning of the target thermal inertial fingerprint model parameters in the thermal inertial fingerprint model library specifically includes: The root mean square error is calculated on the residual sequence to generate a residual energy index. If the residual energy index exceeds the dynamic confidence threshold, a model mismatch trigger signal is generated. In response to the trigger signal, the gradient is corrected by using the residual sequence as error feedback to calculate parameters using the incremental backpropagation algorithm, and the parameters of the target thermal inertial fingerprint model are iteratively updated accordingly.

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