A composite paint layer laser cleaning thickness prediction method based on PSO-SVR

Abstract

The application discloses a kind of composite paint layer laser cleaning thickness prediction method based on group optimization-support vector regression, belong to laser cleaning field. The penalty factor C and kernel function parameter g of support vector regression machine (SVR) are optimized using particle swarm optimization (PSO), a laser paint removal thickness PSO-SVR prediction model with better fitting effect is established, and the accuracy and generalization ability of the model are verified by comparing the prediction results and experimental results of the model, the mapping relationship between laser cleaning process parameters and paint removal thickness is obtained, the laser paint removal thickness can be predicted in advance, which helps to realize effective control of paint removal thickness and coupling optimization of process parameters, the model can provide decision reference and guidance for controllable cleaning of composite paint layer.

Description

Technical Field

[0001] This invention belongs to the field of paint removal thickness prediction technology for composite paint layers in laser paint removal, and specifically relates to a method for predicting the thickness of composite paint layers during laser cleaning based on Particle Swarm Optimization-Support Vector Regression (PSO-SVR). Background Technology

[0002] The outer coating of large components such as aircraft, ships, and subways is generally composed of composite paint, with the surface material typically consisting of aluminum alloy coated with epoxy resin primer and polyurethane topcoat. During service, the coating on the substrate surface may experience various forms of damage, such as aging, cracking, peeling, and flaking, requiring the removal of the original coating and repainting. Considering maintenance costs and safety, the "complete removal" approach to composite paint layers is gradually being replaced by a "partial paint removal" approach, highlighting the need for controllable removal of multi-layered paint structures. Traditional paint removal methods include mechanical grinding, chemical cleaning, high-pressure water jet cleaning, and sandblasting. These methods not only easily damage the substrate but also generate waste liquid, potentially polluting the environment. Moreover, these methods generally suffer from low efficiency and high consumption, insufficient precision in paint layer removal thickness, and poor surface uniformity after paint removal, failing to meet the requirements for controllable removal of composite paint layers.

[0003] Laser cleaning, under appropriate process parameter control, can rapidly remove paint of a specified thickness while achieving high surface quality, making it a valuable new paint removal technology for engineering applications. The paint removal thickness is primarily influenced by the laser cleaning process parameters; by controlling these parameters, the laser paint removal thickness can be altered, thus achieving controllable paint removal. However, traditional laser cleaning parameter selection methods rely on extensive experimental data and experience from engineering practice, making them highly susceptible to the subjective influence of engineers and increasing time, resource, and personnel costs, thereby raising experimental costs. Therefore, for the needs of composite paint layer removal technology, analyzing and predicting the laser paint removal thickness plays a crucial role in achieving controllable cleaning of composite paint layers and optimizing the coupling of process parameters.

[0004] In recent years, numerous scholars have explored the nonlinear relationship between laser cleaning process parameters and paint removal quality, predicting the cleaning quality of the paint layer. Chen Yajun et al. established a mathematical model based on response surface methodology (RSM) regarding the relationship between laser power, scanning speed, pulse frequency, and paint removal depth. Yang Wenfeng et al. used experimental results for regression analysis, employing a quadratic polynomial regression model to construct a mapping relationship between spot overlap rate, laser power, number of scans, and paint removal thickness. Yang Jianian et al. used Design-Expert software to study and obtain the influence of laser power, number of scans, and spot overlap rate on the surface microstructure, composition, and surface roughness after laser paint removal. Hu Shaowu et al. established predictive models between process parameters and cleaning effect evaluation indicators using response regression equations and BP neural networks, respectively. The results showed that the prediction error of the BP neural network was controlled below 5%, exhibiting better generalization ability compared to the response regression model. Most of the above studies utilize experimental results combined with response surface methodology to fit regression equations, which can characterize the true relationship between process parameters and paint layer cleaning thickness to a certain extent. However, the modeling methods suffer from insufficient universality, and the modeling accuracy needs improvement. Predictive models built using neural networks achieve high accuracy, but require a large number of samples. However, laser paint removal experiments have limited sample sizes, thus limiting the effectiveness of such intelligent algorithms. In contrast, Support Vector Regression (SVR) models exhibit strong generalization ability and simple structure when solving prediction problems with limited sample sizes, making them more suitable for predicting the thickness of composite paint layers during laser cleaning. The penalty factor C and kernel function parameter g significantly impact prediction accuracy, but an efficient method for parameter selection is lacking. Particle Swarm Optimization (PSO) is a global random search algorithm that is simpler to operate and has better global search capabilities compared to other traditional algorithms, often used for parameter optimization.

[0005] This invention combines the Particle Swarm Optimization (PSO) algorithm and the Support Vector Machine Regression (SVR) algorithm to propose a method for predicting the thickness of composite paint layers during laser cleaning. This method constructs a support vector regression model between laser cleaning process parameters and paint layer thickness based on experimental results of composite paint laser cleaning. The PSO algorithm is used to optimize the penalty factor and kernel function parameters of the support vector regression model, and the prediction accuracy of the models is compared. A PSO-SVR prediction model with high prediction accuracy is obtained, which can predict the laser paint removal thickness in advance, facilitating effective control of the paint removal thickness and coupled optimization of process parameters. This model can provide decision-making reference and guidance for the controllable cleaning of composite paint layers. Summary of the Invention

[0006] To overcome the shortcomings of existing technologies, this invention provides a method for predicting the thickness of composite paint layers during laser cleaning based on PSO-SVR. Specifically, it uses the Support Vector Regression model optimized by Particle Swarm Optimization algorithm (PSO-SVR) to predict the thickness of the composite paint layer during laser cleaning, thereby achieving accurate prediction of the thickness of the laser paint removed before cleaning and obtaining a paint removal effect that better meets the standards.

[0007] This invention is achieved through the following technical solution: A method for predicting the thickness of composite paint layers by laser cleaning based on PSO-SVR includes the following steps: S1. Initial screening of process parameters and determination of the adjustment range of the parameters to be adjusted. Conduct laser cleaning experiments and record data. Organize the dataset and divide the relevant dataset into training set and test set for data preprocessing. Among them, the laser cleaning process parameters are used as input data to import into the model, and the paint removal thickness value is used as output data to import into the model.

[0008] S2. Model the laser paint removal thickness prediction model. Import the training set after normalization preprocessing into the SVR model and train it to obtain the laser paint removal thickness SVR regression prediction model. S3 and SVR parameters were optimized by using the Particle Swarm Optimization (PSO) algorithm to optimize the penalty function C and kernel function parameter g in the support vector machine regression model, in order to improve the model's prediction accuracy for the thickness of composite paint laser cleaning. S4. Find the optimal parameter combination bestC and bestg to replace C and g in the support vector regression prediction model for composite paint laser cleaning thickness, predict the paint removal thickness in the prediction set, and derive the model.

[0009] Furthermore, the normalization formula for the laser cleaning process parameters in step 2, which are used as input data and the paint removal thickness value as output data, is shown below: In the formula: x represents the laser cleaning process parameters, x min For the minimum value, x max This is the maximum value.

[0010] Furthermore, the specific operations of step 2 are as follows: S2.1 Establish a functional relationship between the predicted paint removal thickness f(x) and its input laser cleaning process parameter x, which is expressed as: In the formula, f (x) represents the paint layer cleaning thickness; φ(x) is the mapping function; w is the weight vector; x is the input vector, x={x1, x2, x3, ..., x...} i} represent four laser cleaning process parameters: laser power, repetition frequency, scanning speed, and defocusing amount, respectively; b is the deviation term.

[0011] S2.2. Based on the principle of minimizing structural risk, the objective function and constraints of the support vector regression model based on the ε-insensitive loss function are as follows: Where: ε is the insensitivity coefficient; c is the penalty factor; ξ i ξ*i is the relaxation factor.

[0012] S2.3. Based on the Lagrange multiplier method and the KKT conditions, introduce the kernel function k(x, x). i The final regression function can be expressed as follows: In the formula: , is the Lagrange multiplier; b is the deviation term.

[0013] Furthermore, in step S2.3, the kernel function k(x, x) i Preferred Gaussian radial basis kernel functions with strong generalization ability: Record it g is the parameter of the kernel function.

[0014] Furthermore, the specific operation of step S3 is as follows: S3.1 Establish the particle velocity and position update formulas: In the formula: d∈[1,D], D represents the population size; k∈[1,K], K represents the number of iterations; s∈[1,S], S represents the particle dimension; This represents the flight speed of the particle in the (k+1)th iteration; Let represent the position of the particle in the (k+1)th iteration, c1 and c2 be the learning factors for the individual and the population, respectively; r1 and r2 ∈ [0, 1] are random constants, and p is the inertia weight. S3.1 Set the initial parameters of the PSO particle swarm algorithm, including the number of position iterations, initial population, learning factor, inertia weight, penalty factor C, and the search range of kernel function parameter g, and randomly generate a set of initial particle velocities and positions. S3.2 Within the search range, each particle optimizes the penalty factor C and the kernel function parameter g. The optimization result of each particle is substituted into the paint removal thickness support vector regression model. The mean square error (MSE) is calculated based on the predicted values ​​and the true values ​​obtained during the training process of the support vector machine regression model for different paint removal thicknesses. The calculation method is as follows: It is used as the fitness function of the particle swarm optimization algorithm, and the fitness value of all particles is calculated; S3.3 For each particle in the algorithm, its corresponding fitness value is compared with its optimal position P. best The corresponding fitness values ​​are compared; if the current position is better, then P is replaced with the current position. best ; For each particle in the algorithm, its fitness value is compared with the fitness value corresponding to its individual best position Gbest. If the better position is better, then Gbest is updated. best ; S3.4 Determine whether the PSO algorithm has reached the termination condition, that is, whether the globally optimal solution has been obtained or the maximum number of iterations has been reached. If the above conditions are met, output the optimal penalty factor bestC and the optimal kernel function parameter bestg. Otherwise, continue iterating and continuously update the velocity and position of the particles.

[0015] Furthermore, p∈[0.6, 0.1], c1, c2∈[1.5, 2].

[0016] Furthermore, the specific operation of step S4 is as follows: S4.1 Replace C and g in the support vector regression prediction model for the thickness of composite paint laser cleaning with the found optimal parameter combinations bestC and bestg; S4.2 Test the paint removal thickness PSO-SVR model using test set data. Input the reserved test set into the trained PSO-SVR model and calculate its root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²). 2 The root mean square error (RMSE) and mean absolute error (MAE) reflect the degree of difference between the predicted values ​​of the paint removal regression model and the actual values ​​obtained from the experiment. The coefficient of determination (R²) 2 This reflects the degree of fit of the PSO-SVR model to the sample. The closer the value is to 1, the better the model's ability to capture information from the data sample. The calculation methods are as follows: S4.3. Verify the prediction accuracy of the laser paint removal thickness PSO-SVR model. If it does not meet the requirements, modify the initialization parameters in PSO and iterate again. If it meets the requirements, output the final prediction result and save the trained paint removal thickness PSO-SVR model.

[0017] Beneficial technical effects of the present invention: This invention combines the Particle Swarm Optimization (PSO) algorithm and the Support Vector Machine Regression (SVR) algorithm to form a PSO-SVR-based method for predicting the thickness of composite paint layers during laser cleaning. Compared with predictions based on engineers' experimental experience and response surface regression, the Support Vector Regression (SVR) algorithm demonstrates strong generalization ability and simple structure when solving small sample problems, making it more suitable for predicting the thickness of composite paint layers during laser cleaning. The penalty factor C and the kernel function parameter g have a significant impact on the prediction accuracy of the SVR model, but an efficient method for selecting them is lacking. The Particle Swarm Optimization (PSO) algorithm is a global random search algorithm that is simpler and has better global search capabilities compared to other traditional algorithms, and is often used for parameter optimization.

[0018] This method constructs a support vector regression model between laser cleaning process parameters and paint layer cleaning thickness based on experimental results of composite paint laser cleaning. The PSO algorithm is used to optimize the penalty factor and kernel function parameters of the support vector machine regression model and compare the prediction accuracy of the model. A PSO-SVR prediction model with high prediction accuracy is obtained, which can predict the laser paint removal thickness in advance, which helps to achieve effective control of paint removal thickness and coupled optimization of process parameters. This model can provide decision reference and guidance for the controllable cleaning of composite paint layers. Attached Figure Description

[0019] The invention will now be further described with reference to the accompanying drawings.

[0020] Appendix Figure 1 This is a schematic diagram of the steps in the prediction method of the present invention; Appendix Figure 2 This is a schematic diagram of the PSO-SVR algorithm established in this invention; Appendix Figure 3 This is a curve showing the variation of paint removal thickness fitness of the PSO-SVR prediction model in this invention. Appendix Figure 4 This is a schematic diagram comparing the true values ​​of the test samples of this invention with the predicted values ​​based on the PSO-SVR model; Appendix Figure 5 This is a schematic diagram comparing the absolute error values ​​of the three models of this invention; Detailed Implementation

[0021] The following are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

[0022] The present invention will now be further described with reference to the accompanying drawings, incorporating preferred embodiments.

[0023] See Figure 1-2 A method for predicting the thickness of composite paint layers in laser cleaning based on PSO-SVR, the specific implementation steps of which include: Step 1 In this embodiment, the experimental sample was selected as an aluminum alloy sheet commonly used for aircraft skin, with a thickness of about 2mm. A 40±3μm white polyurethane topcoat and a 20±3μm green epoxy primer were uniformly sprayed on the surface, and the sample was cut into 50mm×50mm×2mm specimens. Each substrate was laser cleaned only once to eliminate the thermal impact on adjacent cleaning areas.

[0024] We selected laser cleaning process parameters and levels, and designed laser paint removal experiments to measure and record the paint removal thickness under different laser cleaning process parameters. During laser paint removal, changes in defocusing directly affect the laser spot size, which in turn affects the laser energy density. The laser energy density determines the impact and ablation effect of a single laser pulse on the substrate, while the spot overlap rate determines the superposition effect of thermal stress during laser paint removal. These three aspects influence the final effect of laser paint removal.

[0025] In this context, the energy density of a pulsed laser is expressed by power and frequency: E=4P / fπd 2Where: E is the laser energy density; P is the laser power; f is the laser repetition frequency; and d is the spot diameter. The spot diameter is related to the defocusing amount, and the spot overlap rate refers to the degree of overlap between laser spots under the action of the galvanometer oscillation. The spot overlap rate is determined by both the scanning speed and the laser repetition frequency.

[0026] Therefore, there are four main influencing factors for laser paint removal: laser power (P), repetition frequency (f), scanning speed (v), and defocusing amount (h). Based on this, a four-factor, three-level Box-Behnken response surface methodology experiment was designed using the results of single-factor experiments. The level coding design for each factor is shown in Table 1. Based on the factors and levels in the table, a laser paint removal experiment was designed. The laser cleaning system used in the experiment mainly consists of a fiber pulsed laser, a KUKA robot, a laser cleaning machine control system, a dust removal device, and a laser cleaning head. The laser used is an MFP300W acousto-optic Q-switched pulsed fiber laser, and the beam energy follows a Gaussian distribution. The main parameters of the laser cleaning machine are shown in the table below.

[0027] During the cleaning process, the cooling system was kept running throughout to prevent the laser cleaning head from being damaged by overheating. Compressed gas was introduced as a protective gas to prevent dirt and dust from adhering to the lens and damaging the cleaning head. A laser generator was used as the heat source, with a power adjustment range of 0-300W and a wavelength of 1064nm. The laser beam was emitted from the laser head and irradiated the surface of the workpiece to be cleaned. Simultaneously, the galvanometer oscillated, causing the laser spot to expand from a point to a line and then to a surface, ultimately cleaning a 30mm x 40mm area on the workpiece surface.

[0028] After the experiment, a high-precision paint film thickness gauge was used to measure the thickness of the cleaned sample. Multiple measurements were taken and averaged to ensure the scientific validity and accuracy of the data. Before cleaning, five points (the intersection of the four corners and the diagonals) were measured on the paint layer surface to obtain the original paint layer thickness (H1). After cleaning, these points were measured again to obtain the residual thickness (H2). Schematic diagrams of the paint layer cross-sections before and after cleaning are shown below. Figure 3 As shown, the cleaning thickness (H) is the difference between the original paint layer thickness (H1) and the paint layer thickness after cleaning (H2), i.e., H = H1 - H2. The cleaning thickness under different laser cleaning process parameters is expressed as follows: Step 2: To meet the training requirements of the machine learning model and improve its accuracy and generalization ability, 25 more experiments were added to the 29 results obtained from the BBD experiment.

[0029] The data from the two sets of experiments were combined and randomly shuffled to form a training set and a test set. Of the 54 data sets, 40 were used as the training dataset and the remaining 14 as the test dataset. Laser cleaning process parameters (laser power P, repetition frequency f, scanning speed v, and defocusing amount h) were used as input data into the model, while paint removal thickness was used as output data.

[0030] Step 3: Since the laser cleaning process parameters and paint removal thickness have different dimensions and value ranges, the input and output data need to be normalized to bring them to the same order of magnitude. The normalization formula is as follows: In the formula: x is the laser cleaning process parameter, x min For the minimum value, x max This is the maximum value.

[0031] Step 4: Select a suitable kernel function to establish a support vector regression model for the initial laser cleaning process parameters and paint removal thickness, and train the model using the training set data partitioned in Step 2. There are many types of kernel functions for support vector regression models, commonly including linear kernels, polynomial kernels, radial basis function / Gaussian kernels, and sigmoid kernels. Choosing different kernel functions can lead to significant differences in model prediction accuracy. For predicting laser paint removal thickness, experimental comparisons show that the Gaussian radial basis function prediction model has higher accuracy than other types of kernel functions. Based on this, this invention preferably uses the Gaussian radial basis function, which has strong generalization capabilities. Record it For a support vector machine regression model using a Gaussian radial basis function kernel, the main influencing parameters are the penalty function C and the kernel function parameter g. These two parameters determine the learning and generalization ability of the SVR.

[0032] Step 5: The Particle Swarm Optimization (PSO) algorithm is used to optimize the penalty function C and kernel parameter g in the support vector machine regression model to improve the model's prediction accuracy for the thickness of composite paint laser cleaning. The PSO algorithm is inspired by the flight and flocking behavior of birds in search of food, where the particle's velocity determines its flight direction and distance, and its optimal position P... best With the population's optimal position G best The decision is made. The formulas for updating the particle's velocity and position are as follows: In the formula: d∈[1,D], D represents the population size; k∈[1,K], K represents the number of iterations; s∈[1,S], S represents the particle dimension; This represents the flight speed of the particle in the (k+1)th iteration; Let represent the position of the particle in the (k+1)th iteration, c1 and c2 are the learning factors of the individual and the population, respectively; r1, r2∈[0,1] are random constants, and p is the inertia weight; r1, r2∈[0,1] are random constants.

[0033] The initial parameters of the PSO (Particle Swarm Optimization) algorithm are set, including the number of position iterations, initial population, learning factor, inertia weight, penalty factor C, and the search range of the kernel function parameter g. A set of initial particle velocities and positions is randomly generated. Considering the parameter characteristics of laser cleaning thickness prediction, and after multiple optimization experiments, the optimal parameters are: p∈[0.6, 0.1]; c1, c2∈[1.5, 2] are random constants. Experiments have verified that setting the parameters c1, c2, and p within this range results in faster convergence of the PSO algorithm, a smaller fitness function after convergence, and a smaller error between the predicted data and the true value.

[0034] Finally, in MATLAB, the maximum number of generations of the particle swarm optimization algorithm was set to 200, the population size was 20, the penalty factor C∈[0.01, 100], the kernel function parameter g∈[0.01, 100], the local search capability c1=1.5, the global search capability c2=1.7, and 5-fold cross-validation was performed on the training samples; the positions and velocities of the 20 particles in the population were initialized.

[0035] Step 6: Within the search range, each particle optimizes the penalty factor C and the kernel function parameter g. Therefore, the optimization result of each particle is substituted into the paint removal thickness support vector regression model. The mean squared error (MSE) is calculated based on the predicted and true values ​​obtained during the training process of the support vector machine regression model for different paint removal thicknesses. The calculation method is as follows: It is used as the fitness function of the particle swarm optimization algorithm, and the fitness value of all particles is calculated.

[0036] Step 7: For each particle in the algorithm, set its fitness value to its optimal position P. best The corresponding fitness values ​​are compared; if the current position is better, then P is replaced with the current position. best Similarly, update G accordingly. best .

[0037] Step 8: Determine if the PSO algorithm has reached the termination condition, i.e., obtained the globally optimal solution or reached the pre-set maximum number of iterations. If the above conditions are met, output the optimal penalty factor bestC and the optimal kernel function parameter bestg; otherwise, continue to update the particle's velocity and position using the iterative formula in Step 5. See the appendix for the iterative process. Figure 3 As shown, the C and g of the support vector regression prediction model for the thickness of composite paint laser cleaning are replaced with the found optimal parameter combinations bestC and bestg. In this embodiment, the optimal penalty factor C = 14.624 and the optimal kernel function parameter g = 0.7123.

[0038] Step 9: Test the PSO-SVR model after paint removal using the test set data. Import the reserved test set into the trained PSO-SVR model and calculate its root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²). 2 The root mean square error (RMSE) and mean absolute error (MAE) determine the degree of difference between the predicted values ​​of the paint removal regression model and the actual values ​​obtained from the experiment. The coefficient of determination R0 2 This determines the degree of fit of the PSO-SVR model to the samples; the closer the value is to 1, the better the model's ability to capture information from the data samples. The calculation methods are as follows: In the example, the root mean square error (RMSE) between the predicted value and the experimentally obtained true value was 1.738, the mean absolute error (MAE) was 1.5162, and the coefficient of determination R0 was [missing value]. 2 =0.96171. Using MATLAB's visualization and plotting functions, the predicted and experimental curves of the test set are exported. See the appendix for details. Figure 4 .

[0039] Step 10: Verify the prediction accuracy of the laser paint removal thickness PSO-SVR model. If it does not meet the requirements, proceed to step 5, modify the initialization parameters in PSO, and iterate again. If it meets the requirements, output the final prediction result and save the trained paint removal thickness PSO-SVR model.

[0040] The PSO-SVR, SVR, and BPNN regression models were used in MATLAB simulation experiments to predict the paint removal thickness of the test set samples. The experimental results are shown in the table below: Based on the data in the table and the appendix Figure 4-5It can be seen that the PSO-SVR model has a significant advantage in predicting the thickness of composite paint layers during laser cleaning. When predicting paint removal thickness, the root mean square error of PSO-SVR is improved by 0.541 and 1.9339 compared to the standard SVR and BPNN models, respectively, indicating that the prediction results of the PSO-SVR algorithm are closer to the true values ​​than the standard SVR and BPNN models. From the coefficient of determination, the goodness of fit of PSO-SVR is greater than that of SVR and BPNN, indicating that the support vector machine optimized by particle swarm optimization is better able to explain the correlation between laser cleaning process parameters and paint removal thickness than the SVR and BPNN models. This demonstrates that the PSO-SVR prediction model has better predictive performance for the thickness of composite paint layers during laser cleaning, and also shows that SVR parameter optimization plays an important role in improving the accuracy of laser paint removal thickness prediction. This model can provide decision-making reference and guidance for the controllable cleaning of composite paint layers.

[0041] The embodiments described above are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments. Any obvious improvements, substitutions or modifications that can be made by those skilled in the art without departing from the essence of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for predicting the thickness of composite paint layers during laser cleaning based on PSO-SVR, characterized in that: Includes the following steps: S1. Initial screening of process parameters and determination of the adjustment range of the parameters to be adjusted. Conduct laser cleaning experiments and record data. Organize the dataset and divide the relevant dataset into training set and test set for data preprocessing. Among them, the laser cleaning process parameters are used as input data to import into the model, and the paint removal thickness value is used as output data to import into the model. S2. Model the laser paint removal thickness prediction model. Import the training set after normalization preprocessing into the SVR model and train it to obtain the laser paint removal thickness SVR regression prediction model. S3 and SVR parameters were optimized, and the penalty function in the support vector machine regression model was optimized using the particle swarm optimization (PSO) algorithm. C and kernel function parameters g To improve the model's prediction accuracy for the thickness of composite paint laser cleaning; S4. The optimal parameter combinations bestC and bestg are found to replace the support vector regression prediction model for composite paint laser cleaning thickness. C and g The model is derived by predicting the paint removal thickness in the prediction set. The specific steps for step 2 are as follows: S2.1 Establish a system for predicting paint removal thickness f(x) Instead of inputting laser cleaning process parameters x There is a functional relationship between them, which is shown as follows: ； In the formula, f (x) represents the thickness of the paint layer after cleaning; φ(x) It is a mapping function; w It is a weight vector; x It is the input vector. x={x 1 ，x 2 ， x 3 ，…，x i } These represent four laser cleaning process parameters: laser power, repetition frequency, scanning speed, and defocusing amount, respectively. b This is the deviation term; S2.2, Based on the principle of minimizing structural risk, ε The objective function and constraints of the support vector regression model with insensitive loss function are as follows: ； in: ε Insensitivity coefficient; c As a penalty factor; ξ i , It is a relaxation factor; S2.

3. Based on the Lagrange multiplier method and the KKT conditions, introduce a kernel function. k ( x , x i The final regression function is expressed as follows: ； In the formula: , For Lagrange multipliers; b This is the deviation term.

2. The method for predicting the thickness of composite paint layers by laser cleaning based on PSO-SVR according to claim 1, characterized in that: The normalization formula for the laser cleaning process parameters in step 2, which are used as input data and the paint removal thickness value as output data, is shown below: ； In the formula: x These are the laser cleaning process parameters. x min To be the minimum value, x max This is the maximum value.

3. The method for predicting the thickness of composite paint layers by laser cleaning based on PSO-SVR according to claim 1, characterized in that: The kernel function in step S2.3 k ( x , x i Select a Gaussian radial basis kernel function with strong generalization: ； Record it 1 / 2б 2 Kernel function parameters g .

4. The method for predicting the thickness of composite paint layers by laser cleaning based on PSO-SVR according to claim 1, characterized in that: The specific operation of step S3 is as follows: S3.1 Establish the particle velocity and position update formulas: ； In the formula: d ∈[1, D ], D Indicates the size of the population; k ∈[ 1 , K ], K Indicates the number of iterations; s ∈[1, S ], where S represents the dimension of the particle; This represents the flight speed of the particle in the (k+1)th iteration; This indicates the position of the particle in the (k+1)th iteration. c 1 , c 2 These are learning factors for individuals and populations, respectively. r 1 , r 2 ∈[0,1] is a random constant. p It is inertial weight; S3.1 Set the initial parameters of the PSO (Particle Swarm Optimization) algorithm, including the number of position iterations, initial population, learning factor, inertia weight, and penalty factor. C and kernel function parameters g The search range is defined, and a set of initial particle velocities and positions are randomly generated; S3.2 Within the search range, each particle will optimize the penalty factor. C and kernel function parameters g The optimization result of each particle is substituted into the paint removal thickness support vector regression model. The mean square error (MSE) is calculated based on the predicted values ​​and the true values ​​obtained during the training process of the support vector machine regression model for different paint removal thicknesses. The calculation method is as follows: ； It is used as the fitness function of the particle swarm optimization algorithm, and the fitness value of all particles is calculated; S3.3 For each particle in the algorithm, its corresponding fitness value is compared with its optimal position. P best The corresponding fitness values ​​are compared; if the current position is better, it is replaced with the current position. P best ; For each particle in the algorithm, its corresponding fitness value is compared with its optimal position. G best The corresponding fitness values ​​are compared; if the current fitness value is better, then it is updated. G best ; S3.4 Determine whether the PSO algorithm has reached the termination condition, i.e., obtained the globally optimal solution or reached the pre-set maximum number of iterations; if the above conditions are met, output the optimal penalty factor. C best and optimal kernel function parameters g best Conversely, if the velocity and position of the particles are not found, the iteration continues, constantly updating the particle's velocity and position.

5. The method for predicting the thickness of composite paint layers by laser cleaning based on PSO-SVR according to claim 3, characterized in that: The p ∈[0.6, 0.1], c 1 , c 2 ∈[1.5, 2].

6. The method for predicting the thickness of composite paint layers by laser cleaning based on PSO-SVR according to claim 1, characterized in that: The specific operation of step S4 is as follows: S4.1 Replace the support vector regression prediction model for composite paint laser cleaning thickness with the found optimal parameter combinations bestC and bestg. C and g ; S4.2 Test the paint removal thickness PSO-SVR model using test set data. Input the reserved test set into the trained PSO-SVR model and calculate its root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²). 2 The root mean square error (RMSE) and mean absolute error (MAE) reflect the degree of difference between the predicted values ​​of the paint removal regression model and the actual values ​​obtained from the experiment. The coefficient of determination (R²) 2 This reflects the degree of fit of the PSO-SVR model to the sample. The closer the value is to 1, the better the model's ability to capture information from the data sample. The calculation methods are as follows: ； ； S4.

3. Verify the prediction accuracy of the laser paint removal thickness PSO-SVR model. If it does not meet the requirements, modify the initialization parameters in PSO and iterate again. If it meets the requirements, output the final prediction result and save the trained paint removal thickness PSO-SVR model.

Images