Intelligent optimization method for anti-corrosion composite tray coating process based on digital twinning

Abstract

The invention discloses an intelligent optimization method for an anti-corrosion composite tray coating process based on digital twinning, and belongs to the technical field of composite material surface treatment. The method comprises the following steps: constructing a coating microenvironment multi-physics field coupling digital twin model, and realizing real-time data assimilation by adopting ensemble Kalman filtering; establishing a performance degradation prediction model based on photo-oxidative aging, electrochemical corrosion and mechanical wear, and performing state estimation through particle filtering; a radial basis function network and a gradient projection method are adopted to realize reverse derivation of process parameters, and dynamic compensation is implemented through model predictive control; extracting process knowledge by using association rule mining and a hidden Markov model, and performing regularized expression; the model precision is verified through an orthogonal experiment, and continuous optimization is realized by adopting Bayesian model selection and incremental learning. According to the method, full-process digital modeling, precise performance prediction and intelligent parameter optimization of the coating process are realized, and the coating quality consistency and the process optimization efficiency are remarkably improved.

Description

Technical Field

[0001] This invention belongs to the field of composite material surface treatment technology, and in particular relates to an intelligent optimization method for anti-corrosion composite tray coating process based on digital twins. Background Technology

[0002] Composite material pallets are widely used in logistics and chemical storage due to their lightweight, high strength, and corrosion resistance. The coating, as a key barrier against corrosion, directly affects the lifespan and safety of the pallet.

[0003] Existing coating process optimization technologies have the following main shortcomings: Firstly, traditional coating processes rely on empirical parameters and offline adjustments, lacking the ability to perceive and dynamically model the coating microenvironment in real time, making it difficult to achieve precise control of process parameters. Secondly, existing quality monitoring methods are mostly post-event inspections, which cannot predict the final performance during the coating formation process, resulting in defective products having to be reworked or scrapped, causing a waste of resources; Third, the degradation mechanism of coating performance is complex, and existing technologies lack a full life cycle performance evolution model, making predictive maintenance impossible. Problems are often only discovered after the coating fails. Fourth, process optimization often adopts a forward trial-and-error method, which is time-consuming, costly, and difficult to quickly locate the process parameters that cause specific defects, resulting in low optimization efficiency.

[0004] Therefore, there is an urgent need for an intelligent technical solution that can realize digital modeling, real-time optimization, and full lifecycle management of the coating process. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides an intelligent optimization method for anti-corrosion composite pallet coating process based on digital twins. By constructing a multi-level digital twin model, the entire coating process can be monitored, performance predicted, and parameters optimized.

[0006] The present invention adopts the following technical solution: A smart optimization method for anti-corrosion composite pallet coating process based on digital twins, characterized by the following steps: Step S1. Construct a digital twin model of the coating microenvironment: Environmental parameter data, coating characteristic data, spraying process parameter data, and substrate surface condition data were collected. Based on the collected data, the Lagrange particle tracking equation was used to simulate the trajectory of coating droplets, the thin film flow equation was used to describe the coating deposition process, the Kamal-Sourour model was used to characterize the curing reaction kinetics, and the heat and mass transfer coupling equation was used to calculate the temperature field evolution. An ensemble Kalman filter algorithm was used to achieve dynamic assimilation between the model and the measured data. Step S2. Predict the coating performance degradation trend based on time series analysis: A photo-oxidative aging kinetic equation, an electrochemical corrosion diffusion model, and an Archard wear model were constructed to establish a coating health index evaluation system. A particle filter algorithm was used for state estimation and parameter identification, and the remaining service life was predicted through first-arrival time analysis. The optimal maintenance strategy was solved based on dynamic programming. Step S3. Perform reverse derivation and closed-loop optimization of process parameters: A comprehensive coating quality evaluation function is established, and a radial basis function network is used to approximate the nonlinear mapping relationship between performance and parameters. The gradient projection method is used to derive the optimal process parameters from the target performance. Online quality prediction and dynamic compensation are implemented through model predictive control. A Bayesian network is constructed to establish a causal reasoning mechanism between defects and parameters. Step S4. Extract coating process knowledge and express it in a standardized manner: Dynamic time warping is used to align time-series data and extract time-domain, frequency-domain, and time-frequency-domain features; FP-Growth algorithm is used to mine association rules and Hidden Markov Model is used to identify process state transition patterns; Dempster-Shafer evidence theory is used for knowledge fusion to establish a knowledge representation system that combines production rules and ontology. Step S5. Verify the accuracy of the digital twin model and perform continuous optimization: Orthogonal experiments were designed to obtain validation data, and multiple statistical indicators were used to evaluate the model's prediction accuracy. Systematic biases were identified through residual analysis. A Bayesian model was used to select and optimize the model structure, and an elastic weight solidification strategy was employed to achieve incremental learning. A model health score monitoring system was established to trigger a condition-driven retraining mechanism. Steps S1 to S5 form an iterative optimization closed loop, where data and knowledge from each production cycle are used to enhance the accuracy and generalization ability of the digital twin model. Beneficial effects

[0007] 1. Enhanced real-time monitoring capabilities: By constructing a digital twin model of the coating microenvironment, comprehensive real-time monitoring of the coating formation process can be achieved, improving the transparency and controllability of the process.

[0008] 2. Predictive maintenance implementation: The performance degradation prediction model based on time series analysis can identify coating failure risks in advance, transforming passive maintenance into proactive intervention.

[0009] 3. Improved efficiency: By employing reverse derivation and closed-loop optimization techniques, the optimal process parameters can be quickly located, reducing the number of trials and errors and resource waste.

[0010] 4. Knowledge accumulation and reuse: Through knowledge extraction and rule-based expression, scattered process experience is systematized to form reusable digital knowledge assets.

[0011] 5. Improved quality consistency: The dynamic compensation mechanism can respond to process disturbances in real time, ensuring the stability of product quality across different batches. Attached Figure Description

[0012] Figure 1 A flowchart illustrating the steps of the method described in this invention is shown. Detailed Implementation

[0013] Exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0014] Combination Figure 1 This invention provides a smart optimization method for anti-corrosion composite pallet coating process based on digital twins, comprising the following steps: Step S1: Construct a digital twin model of the coating microenvironment A multi-source data acquisition system was deployed on the carbon fiber composite tray coating production line. A temperature and humidity sensor array was arranged in a 500mm × 500mm rectangular grid within the spray booth, employing PT100 platinum resistance temperature sensors (measurement range -20℃ to 150℃, accuracy ±0.1℃) and capacitive humidity sensors (measurement range 0 to 100%RH, accuracy ±2%RH), with a data acquisition frequency of 10Hz. A high-speed industrial camera, using a binocular stereo vision configuration, was mounted at the top and center of the side of the spray booth, with a frame rate of 1000fps and a resolution of 1920 × 1080 pixels. A laser rangefinder was fixed to the spray gun bracket, with a measurement range of 160mm to 450mm, accuracy ±0.05mm, and a sampling period of 1ms. A pressure sensor was installed at the spray gun inlet of the paint supply line, with a range of 0 to 10MPa and an accuracy of 0.25%. A flow meter was installed on the main paint supply line, with a measurement range of 0 to 500mL / min and an accuracy of ±0.1%.

[0015] A multiphysics coupled digital twin model of the coating microenvironment was constructed based on the collected real-time data. The trajectory of the paint droplets in the spraying space after leaving the nozzle was obtained by solving the Lagrange particle tracking equation. ; in: The mass of a single droplet is expressed in kg and is calculated based on the droplet diameter and coating density. This is the droplet velocity vector, in m / s, with an initial value determined by the nozzle exit velocity. Time, in seconds; Air resistance, in N; For gravity, the unit is N. ,in The acceleration vector due to gravity is taken as 9.8 m / s². Buoyancy, unit: N ,in For air density, take 1.205 kg / m³ under standard conditions. The volume is the droplet volume, in m³. The force is Magnus, measured in N, and is generated by the rotation of the droplets.

[0016] Air resistance is modeled using a modified spherical particle drag model: ; in: The drag coefficient is dimensionless and related to the Reynolds number. The windward surface area of ​​the fog droplets, in m². , The diameter of the droplets is in meters (m). For relative velocity, This is the air velocity vector, in m / s.

[0017] The drag coefficient is determined based on the particle Reynolds number: in: is the particle Reynolds number, which is dimensionless; The aerodynamic viscosity is taken as 1.81 × 10⁻ at 20℃. 5 Pa·s.

[0018] The deposition and leveling process of the coating on the substrate surface is described by the thin film flow equation: in: The local thickness of the coating is expressed in meters (m). The velocity of the coating surface is expressed in m / s. The source term represents the droplet deposition rate, in m / s; This is the gradient operator.

[0019] The flow velocity of the coating is given by the approximate lubrication theory: ; in: The dynamic viscosity of the coating is expressed in Pa·s, and its variation with temperature follows the Arrhenius relationship. The pressure inside the coating is expressed in Pa.

[0020] The pressure distribution is determined by the Young-Laplace equation: ; in: The surface tension of the coating is expressed in N / m, with a typical value of 0.025-0.035 N / m. This refers to the density of the coating, expressed in kg / m³. The acceleration due to gravity is 9.8 m / s².

[0021] The temperature field evolution during the coating curing process considers heat transfer, exothermic reaction, and solvent evaporation: in: The specific heat capacity of the coating is expressed in J / (kg·K), with a typical value of 1800-2200 J / (kg·K). Temperature, in Kelvin (K). The value represents the thermal conductivity of the coating, expressed in W / (m·K), ranging from 0.15 to 0.25 W / (m·K). The heat release rate of the curing reaction is expressed in W / m³. The solvent evaporation endothermic rate is expressed in W / m³. The value represents the convective heat transfer rate, expressed in W / m³.

[0022] The curing reaction kinetics were performed using the Kamal-Sourour model: ; in: The degree of curing is dimensionless and ranges from 0 to 1. , The reaction rate constant is expressed in s⁻¹. , This is the reaction order, dimensionless, determined by DSC experiments, with a typical value. =0.3-0.5, =1.5-2.0.

[0023] Temperature dependence of reaction rate constant: ; in: Pre-exponential factor, correspond =1.5×10 6 s⁻¹, correspond =2.0×10 7 s⁻¹; For activation energy, =65 kJ / mol, =70 kJ / mol; The gas constant is 8.314 J / (mol·K); subscript Choose 1 or 2.

[0024] Relationship between reaction exothermic rate and curing rate: ; in: The heat of reaction per unit mass of resin, in J / kg, with a typical value of 350-450 J / g for epoxy resin systems; This represents the resin density, expressed in kg / m³.

[0025] The solvent evaporation rate is controlled by a diffusion model: in: The mass transfer coefficient, in m / s, is determined by the Sherwood number correlation. The evaporation area per unit volume, in m⁻¹; The solvent concentration on the coating surface is expressed in kg / m³. The concentration of solvent in the environment is expressed in kg / m³. The latent heat of vaporization of the solvent is expressed in J / kg.

[0026] The mass transfer coefficient is calculated using the Sherwood number: ; in: These are Sherwood numbers, which are dimensionless. Characteristic length, in meters; The solvent's diffusion coefficient in air is expressed in m² / s. The Reynolds number is dimensionless. Schmidt number, dimensionless. .

[0027] The random distribution of coating defects was simulated using a non-uniform Poisson process, with the defect density function as follows: in: For position Defect density at a location, in m⁻²; Peak defect density, in m⁻²; The coordinates of the center of the high-incidence defect area are in meters. The standard deviation of the defect distribution is expressed in meters (m). This refers to the basic defect density, expressed in m⁻².

[0028] The defect size distribution follows a log-normal distribution: in: Defect radius The probability density function; The mean is logarithmic. is the logarithmic standard deviation.

[0029] The constructed digital twin model achieves data assimilation through ensemble Kalman filtering. The state vector contains discrete node values ​​of the temperature, concentration, and curing degree fields. The observation operator maps the model state to the sensor measurement locations, and the ensemble membership is between 50 and 100. The model is solved discretically using the finite element method, with a spatial mesh using triangular elements (minimum element size 1 mm). The time step is adaptively adjusted according to the CFL conditions. Boundary conditions include no-slip substrate surface, free surface stress equilibrium, and far-field temperature and concentration conditions. Through multiphysics coupling modeling and real-time data assimilation, the digital twin model accurately maps the coating formation process, outputting coating thickness distribution, curing degree distribution, residual stress distribution, and defect distribution maps, providing fundamental data for the performance degradation analysis in step S2.

[0030] Step S2: Predict the coating performance degradation trend based on time series analysis The coating performance degradation prediction uses the output of the digital twin model constructed in step S1 as the initial condition, and combines it with the actual service environment data of the pallet to conduct a full life cycle performance evolution analysis. During the service life of the pallet, performance degradation data is collected through an embedded sensor network and regular inspections. The embedded sensors include a printed circuit board pH sensor (measurement range pH 2-12), a flexible impedance sensor patch (operating frequency 0.01Hz to 100kHz), and a wireless temperature and humidity logger. Regular inspection items include ultrasonic thickness measurement (probe frequency 5MHz, accuracy ±1μm), gloss measurement (60° specular gloss meter, range 0-2000GU), and cross-cut adhesion testing (ISO 2409 standard, rating 0-5).

[0031] Based on the collected multidimensional time-series data, a physical-chemical coupling model for coating performance degradation was constructed. The fracture dynamics of polymer chain segments during photo-oxidative aging follow the following: in: This represents the concentration of polymer chain segments, expressed in mol / m³. The photolysis rate constant is expressed in units of (W / m²)⁻ᵝs⁻¹; Ultraviolet light intensity, measured in W / m², obtained from meteorological data; is the light intensity response order, dimensionless, and ranges from 0.5 to 1.0; is the oxidation rate constant, in m³ / (mol·s); This represents the dissolved oxygen concentration in the coating, expressed in mol / m³.

[0032] The decrease in crosslinking density caused by chain segment breakage affects the mechanical properties of the coating: in: For time The elastic modulus at time, in GPa; This is the initial elastic modulus, in GPa. Crosslinking density, in mol / m³; The initial crosslinking density is expressed in mol / m³.

[0033] Relationship between crosslinking density and chain segment concentration: in: The value represents the overall degradation rate, expressed in s⁻¹, and includes contributions from photolysis and thermal oxidation.

[0034] The electrochemical corrosion process is described using a double-layer model, and the corrosion current density at the coating / metal interface is: in: This represents the corrosion current density, expressed in A / m². Exchange current density, unit A / m², typical value 10⁻ 8 Up to 10⁻ 6 A / m²; is the anode transfer coefficient, dimensionless, with a value of 0.3-0.7; The value is Faraday's constant, 96485 C / mol; This is an overpotential, measured in volts (V). The gas constant is 8.314 J / (mol·K); Temperature, in Kelvin (K).

[0035] The accumulation of corrosion products at the coating / substrate interface leads to coating peeling, and the rate of increase in peeling area is as follows: in: The area to be stripped is in m². , where is the peeling rate constant, in m / s^{0.5}; This is the activation energy for stripping, expressed in J / mol, with a typical value of 40-60 kJ / mol. This is an environmental factor function.

[0036] The environmental factor function takes into account the synergistic effect of pH and chloride ion concentration: in: This is the pH influence coefficient, with a typical value of 0.1-0.3; The chloride ion influence coefficient is expressed in (mol / L). 0 · 5 Typical values ​​are 0.5-1.0; This represents the chloride ion concentration, expressed in mol / L.

[0037] The change in coating impedance as a function of corrosion is characterized using an equivalent circuit model: in: The impedance is a complex impedance, in Ω·cm². The resistance of the solution is expressed in Ω·cm². The resistance of the coating is expressed in Ω·cm². For coated capacitors, the unit is F / cm²; Angular frequency, in rad / s; The imaginary unit; The diffusion index is dimensionless and ranges from 0.5 to 1.0.

[0038] Coating resistance as a function of water absorption rate: in: The initial coating resistance is expressed in Ω·cm². This is the moisture influence coefficient, dimensionless, with a typical value of 2-5; The value represents the water absorption rate, which is dimensionless.

[0039] The water absorption process follows Fick's law of diffusion: in: This is the saturated water absorption rate, dimensionless, with typical values ​​of 0.02-0.05. The value is the water diffusion coefficient, in m² / s. The coating thickness is expressed in meters (m).

[0040] Based on the aforementioned degradation mechanism model, a particle filter algorithm is used for state estimation and parameter identification. The state-space model is represented as follows: in: This is a state vector, containing the degree of curing, crosslinking density, water absorption rate, and peel area; This is the model parameter vector; For observation vectors; This is the state transition function; For observation functions; , These are process noise and observation noise, respectively.

[0041] Particle weight updates employ sequential importance sampling: in: For the first Each particle at time The weights; Let be the likelihood function.

[0042] When the number of effective particles Below the threshold Resampling is performed at certain times, among which The total number of particles is between 500 and 1000.

[0043] The remaining service life of the coating is predicted using first-arrival time analysis: in: Remaining useful life; The current moment; As a health index; This is the failure threshold, typically set to 60% of the initial value.

[0044] The health index is derived by fusing multiple performance indicators: ; in: For the first The current value of each performance metric; Initial value; The weighting coefficients are determined using the analytic hierarchy process (AHP).

[0045] The weight determination process involves constructing a judgment matrix. ,element Indicators relative to indicators Importance: The weight vector is the normalized result of the eigenvector corresponding to the largest eigenvalue. Consistency check metric: in: It is the largest eigenvalue; As a consistency indicator. When Consistency was considered acceptable at the time, among which It is a random consistency index.

[0046] Optimize maintenance decisions based on predicted performance degradation trajectories. Maintenance cost function: in: Cost per instance for preventative maintenance; Number of preventative maintenance operations; Cost per repair maintenance; This refers to the number of corrective maintenance cycles. Unit downtime cost; This represents the total downtime.

[0047] The optimal maintenance strategy is solved using dynamic programming: in: For state At any moment The value function; For maintenance purposes; For action space; For immediate costs; Discount factor; Let be the state transition probability.

[0048] Through the aforementioned physicochemical coupling modeling and data-driven prediction, accurate prediction of coating performance and optimized formulation of maintenance strategies were achieved. The prediction results include degradation curves of various performance indicators, remaining lifetime distribution, and optimal maintenance time windows. This information will guide the adjustment of process parameters in step S3, forming a prediction-optimization closed-loop control.

[0049] Step S3: Perform reverse derivation and closed-loop optimization of process parameters. The process parameter optimization targets the coating performance requirements predicted in step S2, and combines the real-time feedback from the digital twin model in step S1 to construct an inverse mapping mechanism from performance to parameters. The optimization process adopts a hierarchical architecture, with the upper layer performing global optimization and the lower layer implementing local control to ensure that the parameters converge quickly to the optimal region.

[0050] Establish a comprehensive coating quality evaluation function, mapping multi-dimensional performance indicators to a single optimization objective: in: This is the overall quality loss function; For the first Target values ​​for each performance metric; This is the actual value; Let be the weighting coefficient, satisfying ; This is the regularization coefficient, typically ranging from 0.01 to 0.1. This is a penalty item for process stability.

[0051] The process stability penalty term is defined as follows: in: For the first Stability weights of each process parameter; , These are the standard deviation and mean of the parameter, respectively. This represents the number of process parameters.

[0052] The nonlinear mapping relationship between coating performance and process parameters is approximated using a radial basis function network: in: For the first One performance indicator; For output weights; These are radial basis functions; This is a vector of process parameters; For the first Each basis function center; The number of basis functions; It is the Euclidean norm.

[0053] The radial basis functions are of Gaussian type. ; in: Radial distance; The width of the basis functions is determined through cross-validation.

[0054] Basis function centers are selected from historical data using K-means clustering, and output weights are calculated using the least squares method. ; in: For the first A weight vector for each performance metric; To design a matrix, elements ; This is a regularization parameter to prevent overfitting; It is the identity matrix; This is the performance value vector of the training samples.

[0055] The reverse derivation uses the gradient projection method to search for the optimal process parameters from the current performance state: in: For the first The parameter values ​​for the next iteration; For the projection operator, the parameters are constrained within the feasible region. Inside; The step size is adaptively adjusted using the Armijo criterion. This represents the gradient of the objective function with respect to the parameters.

[0056] Gradient calculation is performed using the chain rule: in: Obtained through the analytic derivative of the radial basis function network.

[0057] Feasibility region constraints include upper and lower limits for individual parameters and coupling constraints between parameters: in: , For the first The lower and upper limits of each parameter; This is the constraint function vector.

[0058] Typical coupling constraints include the coordination between spraying speed and pressure: in: The speed of the spray gun movement is expressed in m / s. Spraying pressure, in MPa; Maximum paint flow rate, in mL / min.

[0059] Temperature and viscosity compatibility constraints: in: For temperature The viscosity of the coating below; This represents the maximum viscosity allowed for atomization.

[0060] Online quality prediction is based on process data within a sliding time window: in: For the predicted final performance; For prediction models; The average value of parameters within the time window; The standard deviation of the parameter; This is the environment state vector.

[0061] The prediction model employs an ensemble learning approach, fusing the prediction results from multiple base learners: in: For the first Individual base learners, including random forest, support vector regression, and neural networks; The combined weights are determined through validation set performance. The number of base learners.

[0062] Dynamic compensation control employs a model predictive control framework to optimize the control sequence within a finite time domain. in: For control input (process parameter adjustment amount); For predicting output; For reference trajectory; For prediction in the time domain; To control the time domain; , This is the weight matrix; To control the increment.

[0063] The system dynamic model uses a linearized state-space representation: in: It is a state vector; For measurable disturbances; , , , The system matrix is ​​obtained through system identification.

[0064] The constraints are transformed into linear inequalities: The optimization problem is solved by quadratic programming to obtain the optimal control sequence. Only the first control action is executed, and the optimization is restarted in the next time step to achieve rolling optimization.

[0065] Defect diagnosis and parameter correlation establish a causal inference mechanism through Bayesian networks: in: For defects Time parameters The posterior probability of anomalies; The conditional probability that abnormal parameters lead to defects; This represents the prior probability of parameter anomalies. This represents the marginal probability of the defect occurring.

[0066] Conditional probabilities are obtained through statistical learning from historical data and updated using Beta-Binomial conjugate priors. in: , These are prior parameters; To observe parameters Abnormal and defective The number of times; For parameters Total number of anomalies.

[0067] By constructing the correlation strength matrix between the defect and the parameter: in: The Phi correlation coefficient ranges from -1 to 1, with a larger absolute value indicating a stronger correlation.

[0068] Based on the correlation strength matrix, key parameters causing specific defects are quickly located, and strongly correlated parameters are adjusted first. The adjustment strategy adopts a hierarchical response: in: This represents the maximum adjustment range; It is a symbolic function.

[0069] Through the aforementioned reverse derivation and closed-loop optimization mechanism, rapid mapping and dynamic control from target performance to process parameters are achieved. The optimization results include optimal parameter combinations, parameter adjustment sequences, and defect-parameter correlation maps. This information forms a closed-loop feedback with the real-time monitoring in step S1 and the performance prediction in step S2, while also providing case data for knowledge extraction in step S4.

[0070] Step S4: Extract coating process knowledge and express it in a standardized manner. Process knowledge extraction is based on the optimization cases accumulated in step S3 and the process data generated in steps S1 and S2. Hidden process patterns are discovered through data mining and machine learning methods. The knowledge extraction process adopts a hierarchical architecture: the bottom layer performs data preprocessing and feature engineering, the middle layer performs pattern recognition and rule mining, and the top layer realizes knowledge fusion and conflict resolution.

[0071] In the data preprocessing stage, multi-source heterogeneous data are standardized and aligned. Time-series data are aligned using a dynamic time warping algorithm. in: For sequence The former Points and sequences The former The regular distance between points; For point and The Euclidean distance; For sequence The One data point; For sequence The One data point; , For sequence indexes; regularized paths are obtained through backtracking.

[0072] Feature extraction employs methods in the time domain, frequency domain, and a combination of time and frequency domains. Time-domain features include statistical measures: in: The mean; Standard deviation; It is a skewness, dimensionless; Kuroduality is dimensionless. The number of samples; For the first Each sample value.

[0073] Frequency domain features are extracted using Fast Fourier Transform: in: For the first in the frequency domain Complex values ​​of each frequency component; For the time-domain signal, the first One sampling point; The imaginary unit, ; For frequency index, values ​​range from 0 to... ; For time index, values ​​range from 0 to... .

[0074] Main frequency and its amplitude: in: Main frequency, in Hz; Main frequency amplitude; For frequency The amplitude spectrum at the location; This represents the independent variable that makes the function reach its maximum value.

[0075] The time-frequency domain features are obtained using wavelet packet decomposition, and the energy distribution is as follows: in: For the first The energy of the layer, expressed as the square of a signal unit; For the first Layer Wavelet coefficients; For coefficient index.

[0076] Association rule mining employs the FP-Growth algorithm to construct a frequent pattern tree. Itemset support calculation: in: For itemsets The degree of support is dimensionless. For containing itemsets The number of transactions; This represents the total number of transactions.

[0077] Confidence level definition: in: The confidence level of the rule; For itemsets and The union of; It indicates an implication relationship.

[0078] Effectiveness of the improvement evaluation rules: in: To increase the degree, dimensionless; For conditional probability; The marginal probability is represented by a lift greater than 1, which indicates a positive correlation; a lift equal to 1 indicates independence; and a lift less than 1 indicates a negative correlation.

[0079] For continuous variables, fuzzy association rules are used. A fuzzy set of linguistic variables for temperature is defined as follows: in: For temperature The membership degree of the "low temperature" fuzzy set takes a value between 0 and 1; Temperature value, in °C.

[0080] Fuzzy support and confidence: in: For fuzzy support; For fuzzy confidence; For the first Sample For fuzzy sets Membership degree; For the first Sample For fuzzy sets Membership degree; This indicates the operation of finding the minimum value; The total number of samples.

[0081] The decision tree is constructed using the CART algorithm, with the Gini index as the node splitting criterion. in: For dataset The Gini index is dimensionless. For the first The proportion of class samples to the total sample; This represents the total number of categories.

[0082] feature Gini gain: in: Features Gini gain; Features The set of all possible values; Features Values A subset of; For subset The number of samples; This represents the total number of samples; For subset The Gini index.

[0083] Pruning uses a cost complexity criterion: ; in: For trees The cost complexity; For trees The cost of misclassification; The complexity parameter is dimensionless and determined through cross-validation. For trees The number of leaf nodes.

[0084] Hidden Markov Models are used for process state transition pattern recognition. Model parameters: ; in: For the set of model parameters; This is the state transition probability matrix; The observation probability matrix; This is the initial state probability vector.

[0085] Elements of the state transition probability matrix: ; in: From state Transition to state The probability of; For a moment The hidden state; , The state in the state space; This represents conditional probability.

[0086] Observation probability: ; in: In the state The following observations The probability of; For a moment Observed values; It is a value in the observation space.

[0087] Initial probability: ; in: The state at the initial moment The probability of; This represents the initial state.

[0088] Forward probability: ; in: For a moment In state And the observation sequence is The probability of.

[0089] Backward probability: ; in: From time status To begin, generate subsequent observation sequences. The probability of; This represents the total length of the observation sequence.

[0090] Parameter update formula: ; in: The updated state transition probability; For a moment In state And at any time In state The probability of; For a moment In state The probability of.

[0091] Case similarity calculation: ; in: For example and Global similarity; For the first The weights of each feature satisfy... ; For the first Local similarity function of each feature; , Case studies , The One eigenvalue; The total number of features.

[0092] Local similarity of numerical features: ; in: Similarity for numerical features; , It consists of two values; The range of values; It should be a small positive number, typically 0.001, to avoid division by zero; It represents the absolute value.

[0093] Arc consistency update for knowledge consistency check: in: For the updated variables The range of values; The original value range; For variables The range of values; For variables and The constraints between them; The constraints satisfy the judgment function; This represents the intersection operation of sets; A quantifier indicating existence.

[0094] Evidence fusion formula: ; in: For the set after merging The basic probability assignment; , These are two sets of evidence sources. , The basic probability assignment; The conflict coefficient; This represents the intersection operation of sets; This represents the empty set.

[0095] Calculation of confidence factors for production rules: ; in: As evidence For the hypothesis The confidence factor ranges from -1 to 1; This is a trust metric, with values ​​ranging from 0 to 1. This is a measure of distrust, ranging from 0 to 1.

[0096] Through the fully defined knowledge extraction and expression mechanism described above, process experience is transformed into structured knowledge assets. All parameters and symbols have been clearly explained, ensuring the accuracy and executability of knowledge rules.

[0097] Step S5: Verify the accuracy of the digital twin model and perform continuous optimization. Model validation and optimization focus on the complete digital twin system constructed in steps S1 to S4. Through systematic validation experiments and continuous feedback updates, the model's predictive accuracy and engineering applicability are ensured. The validation process employs a hierarchical validation strategy, including three levels: unit validation, integration validation, and system validation. The optimization process involves targeted improvements based on the validation results.

[0098] During the unit validation phase, the accuracy of each sub-model was evaluated. An orthogonal experiment was designed to obtain the validation dataset. Experimental factors included spraying pressure (3 levels: 2.5, 3.5, 4.5 MPa), spray gun speed (3 levels: 0.3, 0.5, 0.7 m / s), paint viscosity (3 levels: 600, 900, 1200 mPa·s), and ambient temperature (3 levels: 15, 25, 35°C). An L9(3^4) orthogonal array was used to arrange the experiments. Each experiment was repeated three times, and coating thickness, porosity, surface roughness, and adhesion were measured.

[0099] Quantitative evaluation of model prediction accuracy uses multiple statistical indicators: in: Mean absolute error; This is the root mean square error; Mean absolute percentage error, in % For the first Measured values ​​of a sample; The corresponding predicted value; To verify the total number of samples.

[0100] The coefficient of determination evaluates the explanatory power of the model. in: The coefficient of determination, ranging from 0 to 1; It is the sum of squared residuals; The total sum of squares; This represents the average of the measured values.

[0101] Coverage verification of the prediction interval: ; in: To predict the probability of interval coverage; As an indicator function, when the measured value Falling within the prediction range Internal time ,otherwise ; This is the half-width of the predicted interval.

[0102] Average width of the prediction interval: in: This represents the average prediction interval width.

[0103] The comprehensive evaluation indicators balance accuracy and uncertainty. in: For coverage width criteria; This is the penalty coefficient, ranging from 1 to 10; This is a shape parameter, typically 50. The target coverage rate is typically set to 0.95. is the base of the natural logarithm.

[0104] Error distribution analysis identifies systematic biases. The statistical characteristics of the residuals are calculated. in: For the first The residuals of each sample; The mean of the residuals; This represents the standard deviation of the residuals.

[0105] The normality test uses the Jarque-Bera statistic: ; in: Jarque-Bera statistics; This refers to the residual skewness. This represents the residual kurtosis. When... The normality hypothesis is rejected.

[0106] The autocorrelation test was performed using the Durbin-Watson statistic: in: The Durbin-Watson statistic ranges from 0 to 4; values ​​close to 2 indicate no autocorrelation, values ​​close to 0 indicate positive autocorrelation, and values ​​close to 4 indicate negative autocorrelation.

[0107] Heteroscedasticity was tested using the White test, and an auxiliary regression was constructed:

[0108] in: For the first The first sample One explanatory variable; These are the regression coefficients; This is the error term; The number of explanatory variables. Test statistic. ,in The coefficient of determination for auxiliary regression, This represents the number of independent variables in the auxiliary regression.

[0109] Integrated validation assesses the synergistic effect among sub-models. Define interface consistency metrics: in: For interface consistency, the value ranges from 0 to 1; Output for the upstream model; Input for downstream models; It is the vector norm.

[0110] Information transmission delay measurement: ; in: Information transmission delay, measured in milliseconds (ms). The time of transmission; For the time of reception; For processing time.

[0111] System verification employs scenario testing, designing typical and extreme operating conditions. Typical operating conditions include normal production, batch changeover, and environmental fluctuation scenarios; extreme operating conditions include equipment failure, raw material anomalies, and sudden environmental changes. Verification metrics include: ; in: For robustness indicators; The number of scenarios successfully processed; This represents the total number of scenes.

[0112] Response time assessment: ; in: The response time is at the 95th percentile. For the first Response time for this request; Percentile function; The total number requested.

[0113] Model optimization based on validation results employs an adaptive update strategy. Error-driven parameter tuning: in: , These are the model parameters before and after the update, respectively; For parameter adjustment amount; The learning rate is used, and an adaptive strategy is employed. For loss function For parameters The gradient; The regularization coefficient is used. These are the prior parameter values.

[0114] The adaptive adjustment of the learning rate uses the AdaGrad algorithm: ; in: For a moment The learning rate; This is the initial learning rate, typically 0.01. For historical gradient sum of squares; For a moment The gradient; This is a smoothing term, typically with a value of 1e-8.

[0115] Model structure optimization employs Bayesian model selection: in: For given data The lower model The posterior probability; For the model The marginal likelihood; This represents the model's prior probability. This represents the total number of candidate models.

[0116] Marginal likelihood is calculated using the Laplace approximation: in: For the model Maximum a posteriori parameter estimation; For parameter dimensions; It is the Hessian matrix with negative logarithmic posterior.

[0117] Incremental learning updates employ a flexible weight fixation strategy to protect important parameters. in: This is the total loss function; For the loss of new data; For the first The importance weights of each parameter; This is a reference value for the parameter.

[0118] Parameter importance is estimated using the Fisher information matrix: in: For the first Fisher information for each parameter; Represents the input distribution Expectations; This represents the conditional probability of the model.

[0119] Model version management uses semantic version control: in: The primary version number is added during structural changes. This is the minor version number, added when features are enhanced; This is a revision number, added during defect repair.

[0120] Real-time tracking of performance monitoring metrics: in: The model health score ranges from 0 to 100. Score for accuracy; For stability score; Score for efficiency; , , These are the weighting coefficients.

[0121] Conditions for triggering retraining: in: This is a concept drift detection index; This is the drift threshold, typically 0.3.

[0122] Through the aforementioned systematic verification and optimization mechanisms, the digital twin model is ensured to maintain high accuracy and reliability at all times. Verification results are fed back to steps S1-S4, forming a complete closed-loop optimization system. Each step works collaboratively: real-time data from step S1 provides the basis for degradation analysis in S2; prediction results from S2 guide parameter optimization in S3; optimization cases from S3 enrich the knowledge base of S4; knowledge rules from S4 improve the modeling accuracy of S1; and verification in S5 ensures continuous improvement of the entire system, ultimately achieving intelligent upgrading and full lifecycle optimization management of the coating process.

[0123] In summary, this invention, by constructing a digital twin system for the entire coating process, achieves a shift from passive quality control to proactive process optimization, providing a systematic solution for the intelligent upgrading of composite material coating processes. This method is not only applicable to anti-corrosion composite tray coating processes but can also be extended to other coating process fields, demonstrating broad application prospects.

[0124] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Obviously, those skilled in the art can make various modifications and variations to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention also intends to include these modifications and variations.

Claims

1. A method for intelligent optimization of anti-corrosion composite pallet coating process based on digital twin, characterized in that, Includes the following steps: Step S1: Construct a digital twin model of the coating microenvironment, collect multi-source heterogeneous data of the entire coating process, construct a droplet motion model based on the Lagrange particle tracking equation, a coating deposition model based on the thin film flow equation, a curing kinetic model based on the Kamal-Sourour model, and a heat and mass transfer coupling model, and use the ensemble Kalman filter algorithm to achieve data assimilation. Step S2: Based on time series analysis, predict the coating performance degradation trend, establish photo-oxidative aging kinetic equation, electrochemical corrosion diffusion model and mechanical wear model, use particle filtering algorithm for state estimation, and predict the remaining service life through first arrival time analysis; Step S3: Perform reverse derivation and closed-loop optimization of process parameters, construct a radial basis function network to map the relationship between performance and parameters, use the gradient projection method to reverse derive process parameters, and implement dynamic compensation through model predictive control; Step S4: Extract coating process knowledge and express it in a regularized manner, use the FP-Growth algorithm to mine association rules, use a hidden Markov model to identify state transition patterns, and use Dempster-Shafer theory to perform knowledge fusion. Step S5: Verify the accuracy of the digital twin model and continuously optimize it. Design orthogonal experiments to verify the model accuracy, use a Bayesian model to select the optimization structure, and achieve incremental learning through an elastic weight solidification strategy.

2. The method according to claim 1, characterized in that, The droplet motion model in step S1 is obtained by solving the Lagrange particle tracking equation, which states that the derivative of the droplet mass and velocity vector with respect to time is equal to the sum of air resistance, gravity, buoyancy, and Magnus force. The air resistance is proportional to the drag coefficient, air density, droplet frontal area, and the square of the relative velocity.

3. The method according to claim 1, characterized in that, The curing kinetic model in step S1 adopts the form of autocatalytic kinetics. The derivative of the degree of curing with respect to time is equal to the product of two reaction rate constants and the degree of curing and the uncured portion. The reaction rate constants follow the Arrhenius law.

4. The method according to claim 1, characterized in that, The health index in step S2 is defined as the weighted sum of the ratios of the current value to the initial value of the coating performance indicators, which include coating impedance modulus, gloss, adhesion, and coating thickness.

5. The method according to claim 1, characterized in that, The radial basis function network in step S3 represents the performance index as a linear combination of multiple radial basis functions. Each basis function is a Gaussian function of the Euclidean distance between the process parameter vector and the center of the basis function. The output weights are solved by the least squares method.

6. The method according to claim 1, characterized in that, The gradient projection method in step S3 updates the process parameters iteratively. In each iteration, the current parameters are moved along the negative gradient direction of the objective function by a certain step size and projected into the feasible region. The step size is adaptively adjusted using the Armijo criterion.

7. The method according to claim 1, characterized in that, In step S4, the association rule lift is defined as the ratio of rule confidence to consequent support, representing the association strength between the antecedent and consequent; a value greater than 1 indicates a positive correlation.

8. The method according to claim 1, characterized in that, In step S5, the correlation coefficient between the model's predicted value and the measured value is calculated as the health score. When the health score is below 0.7 for three consecutive batches, model retraining is triggered.

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