A PMMA thick plate laser cutting quality prediction method based on CEO-LSSVM

Abstract

The present application relates to the technical field of laser cutting, and more particularly to a PMMA thick plate laser cutting quality prediction method based on CEO-LSSVM. The present application combines a chaotic evolutionary algorithm with a least squares support vector machine to construct a CEO-LSSVM laser cutting quality prediction model for a PMMA thick plate laser cutting process, which can effectively establish a nonlinear mapping relationship between cutting process parameters and cutting cross-section quality evaluation index values. The present application uses a chaotic evolutionary algorithm to optimize the penalty factor and kernel function parameters in the LSSVM prediction model, improves the rationality of model parameter selection, enhances the global search capability and generalization capability of the model, and realizes fast and accurate prediction of the cutting surface roughness and cutting seam perpendicularity in the PMMA laser cutting process, thereby providing technical support for laser cutting process parameter optimization, cutting quality control and high-quality PMMA thick plate processing.

Description

Technical Field

[0001] This invention relates to the field of laser cutting technology, and in particular to a method for predicting the quality of thick PMMA plates laser cutting based on CEO-LSSVM. Background Technology

[0002] Polymethyl methacrylate (PMMA) is a typical transparent polymer material with high light transmittance, light weight, good weather resistance, excellent insulation properties, and easy processing and shaping. It is widely used in advertising signage, architectural decoration, optical displays, automotive interior and exterior trim, and rail transportation. With the continuous expansion of PMMA sheet applications, the requirements for cutting dimensional accuracy, cut surface quality, and processing stability in medium-thick PMMA components are constantly increasing. During the cutting process, it is not only necessary to ensure that the material is stably cut through, but also to focus on controlling the surface roughness and kerf perpendicularity of the cut surface to meet the requirements of subsequent assembly, bonding, and appearance quality.

[0003] Laser cutting technology offers advantages such as non-contact processing, narrow kerf, relatively small heat-affected zone, high processing efficiency, and high flexibility, making it a crucial method for cutting PMMA sheets. By rationally controlling process parameters such as laser power, cutting speed, auxiliary gas pressure, defocusing amount, and focal point position, the forming quality of the PMMA cut surface can be improved to some extent. However, PMMA is a heat-sensitive polymer material, prone to complex thermal behaviors such as melting, vaporization, thermal decomposition, and recasting during laser cutting. When process parameters are not properly matched, the cut surface is prone to problems such as obvious striations, molten slag, increased surface roughness, a kerf that is wider at the top and narrower at the bottom, and decreased perpendicularity, affecting the processing accuracy and service performance of PMMA components.

[0004] Currently, quality control in the laser cutting of thick PMMA plates mainly relies on empirical experiments, single-factor experiments, or orthogonal experiments. These methods determine the optimal process window by changing processing parameters and measuring the cutting results. While these methods can reveal certain process patterns, they suffer from drawbacks such as requiring numerous experiments, high material consumption, long parameter optimization cycles, and difficulty in describing the nonlinear coupling relationships among multiple factors. Particularly in the laser cutting process of thick PMMA plates, laser power, cutting speed, and defocusing amount collectively affect the heat accumulation and material removal state of the cut surface, resulting in a complex nonlinear relationship between surface roughness and kerf perpendicularity. Relying solely on human experience makes rapid and accurate quality prediction difficult.

[0005] In recent years, machine learning methods have received widespread attention for predicting laser processing quality and optimizing process parameters. Least Squares Support Vector Machines (LSSVMs) possess strong small-sample learning capabilities, good nonlinear mapping ability, and high computational efficiency, making them suitable for establishing predictive models between laser cutting process parameters and the quality evaluation indicators of the cut surface. However, the predictive performance of traditional LSSVM models is significantly affected by hyperparameters such as penalty factors and kernel function parameters. Inappropriate parameter selection can easily lead to insufficient model generalization ability and unstable prediction accuracy. Therefore, it is necessary to introduce optimization algorithms to optimize the LSSVM model parameters to improve the model's prediction accuracy and stability for the laser cutting quality of PMMA thick plates.

[0006] Existing technologies employ intelligent optimization algorithms such as Particle Swarm Optimization (PSO) and Whale Optimization (WOA) to optimize the parameters of LSSVM and SVR prediction models, aiming to improve laser processing quality. However, these methods often use cutting width, cut penetration, or a single cutting quality index as the prediction object, typically modeling only a single output such as surface roughness, without considering the synergistic relationship between surface roughness and kerf perpendicularity during PMMA thick plate laser cutting. When both surface roughness and kerf perpendicularity need to be controlled simultaneously as quality evaluation indicators of the cutting section, existing single-index prediction models cannot account for the prediction errors of both quality indicators, failing to provide accurate quality prediction basis for optimizing PMMA thick plate laser cutting process parameters. Summary of the Invention

[0007] The technical problem to be solved by this invention is: how to simultaneously predict the surface roughness and kerf perpendicularity during the laser cutting of PMMA thick plates, and improve the stability and reliability of LSSVM prediction model parameter optimization under the condition that the prediction errors of the two quality evaluation indicators of the cutting section are controlled.

[0008] This invention is achieved through the following technical solution: S1: Collect test data for laser cutting of PMMA thick plates. The test data includes laser cutting process parameters and cut surface quality evaluation index values. Among them, the laser cutting process parameters include laser power, cutting speed, and defocusing amount. The cut surface quality evaluation index values ​​include the cut surface roughness value and the cut perpendicularity value. The laser cutting process parameters are used as input parameters, and the cut surface quality evaluation index values ​​are used as output parameters. Perform data preprocessing on the collected test data, including outlier data removal and missing data supplementation.

[0009] S2: Divide the experimental data into training set and test set, and standardize the training set and test set. Standardization eliminates the impact of differences in the units and numerical ranges of different input parameters on the model training accuracy, resulting in standardized training set and standardized test set.

[0010] S3: Based on the standardized training set, establish an LSSVM prediction model that simultaneously outputs the surface roughness and kerf perpendicularity of the cut surface. The LSSVM prediction model is used to characterize the nonlinear mapping relationship between laser cutting process parameters and the quality evaluation index values ​​of the cut section.

[0011] S4: The Chaotic Evolution Optimization (CEO) algorithm is used to optimize the model parameters of the LSSVM prediction model to obtain the optimal parameter combination of the LSSVM prediction model. The optimization variable of the CEO algorithm is the LSSVM prediction model parameter vector, which includes a penalty factor and kernel function parameters. The optimal penalty factor and optimal kernel function parameters are obtained through population iteration. The Chaotic Evolution Optimization algorithm uses the prediction error of the standardized training set as the fitness function and minimizes the fitness function as the optimization objective.

[0012] S5: Substitute the optimal parameter combination of the LSSVM prediction model obtained in step S4 into the LSSVM prediction model to obtain the CEO-LSSVM laser cutting quality prediction model. Then, use the standardized training set to train the CEO-LSSVM laser cutting quality prediction model so that the model learns the nonlinear relationship between the laser cutting process parameters and the quality evaluation index value of the cutting section.

[0013] S6: Input the laser cutting process parameters from the standardized test set into the trained CEO-LSSVM laser cutting quality prediction model, output the corresponding standardized cutting surface roughness prediction value and standardized kerf perpendicularity prediction value, and perform de-standardization on the standardized prediction values ​​(standardized cutting surface roughness prediction value and standardized kerf perpendicularity prediction value) to obtain the cutting surface roughness prediction value and kerf perpendicularity prediction value in actual dimensions; determine whether the CEO-LSSVM laser cutting quality prediction model meets the set model prediction accuracy requirements based on the cutting surface roughness prediction value and kerf perpendicularity prediction value in actual dimensions. If the model prediction accuracy requirements are met, the final CEO-LSSVM laser cutting quality prediction model is obtained; if the model prediction accuracy requirements are not met, re-enter step S4 until the CEO-LSSVM laser cutting quality prediction model meets the set model prediction accuracy requirements.

[0014] The prediction accuracy of the aforementioned model includes the prediction accuracy of the cutting surface roughness, the prediction accuracy of the kerf perpendicularity, and the prediction accuracy of the comprehensive index. Specifically, the prediction accuracy of the cutting surface roughness is calculated by comparing the predicted value of the cutting surface roughness with the actual measured value, and calculating the root mean square error, mean absolute percentage error, and coefficient of determination for both. The prediction accuracy of the kerf perpendicularity is calculated by comparing the predicted value of the kerf perpendicularity with the actual measured value, and calculating the root mean square error, mean absolute percentage error, and coefficient of determination for both. The prediction accuracy of the comprehensive index includes the comprehensive root mean square error, the comprehensive mean absolute percentage error, and the comprehensive coefficient of determination. The comprehensive root mean square error is obtained by weighting the two values ​​of the calculated root mean square error of the cutting surface roughness prediction accuracy and the root mean square error of the kerf perpendicularity prediction accuracy, with a preferred weighting coefficient of 0.5. The comprehensive coefficient of determination is obtained by averaging the sum of the coefficients of determination for the calculated cutting surface roughness prediction accuracy and the coefficients of determination for the calculated kerf perpendicularity prediction accuracy.

[0015] The model prediction accuracy requirements can be set according to actual needs. Thresholds for the root mean square error (RMSE), mean absolute percentage error (MAS), coefficient of determination (CAD), and combined RMSE, MAS, and CAD can be set separately. For example, the CAD and CAD thresholds can both be set to 0.9; the MAS threshold can be set to 5%; and the CAD threshold can be set to 4%. The RMSE and CAD thresholds can be preset based on the actual dimensions of the cutting surface roughness and kerf perpendicularity, as well as the process quality requirements.

[0016] When the calculated root mean square error, mean absolute percentage error, comprehensive root mean square error, and comprehensive mean absolute percentage error are all less than the corresponding set thresholds, and the coefficient of determination threshold and comprehensive coefficient of determination threshold are both greater than the corresponding set thresholds, then the CEO-LSSVM laser cutting quality prediction model meets the set model prediction accuracy requirements; otherwise, it does not meet the model prediction accuracy requirements, and it is necessary to re-enter step S4 until the requirements are met.

[0017] Once the final CEO-LSSVM laser cutting quality prediction model is obtained, the process parameters for laser cutting of thick PMMA plates to be predicted can be input into the final CEO-LSSVM laser cutting quality prediction model to obtain the predicted values ​​of the cutting surface roughness and kerf perpendicularity under the combination of process parameters. Based on the prediction results, it is determined whether the combination of process parameters meets the PMMA laser cutting section quality evaluation index. After obtaining the predicted values ​​of the cutting surface roughness and kerf perpendicularity, the predicted values ​​are compared with the preset cutting section quality evaluation index thresholds (cutting surface roughness threshold and kerf perpendicularity threshold). When both the predicted values ​​of the cutting surface roughness and kerf perpendicularity are not greater than the preset cutting section quality evaluation index thresholds, it is determined that the current laser cutting process parameters meet the PMMA thick plate cutting section quality evaluation index; otherwise, it is determined that the current laser cutting process parameters do not meet the cutting section quality evaluation index, and the laser cutting process parameters are readjusted, thereby providing a basis for the optimization of PMMA thick plate laser cutting process parameters, cutting quality prediction, and processing control.

[0018] In step S2, the ratio of the training set to the test set is 2:1.

[0019] The LSSVM prediction model includes a sub-model for predicting the surface roughness of the cut surface and a sub-model for predicting the perpendicularity of the cut. The parameter vector of the LSSVM prediction model... Represented as:

[0020] in, and These are the penalty factor and kernel function parameters of the sub-model for predicting the surface roughness of the cut surface, respectively. and These are the penalty factor and kernel function parameters for the cut perpendicularity prediction sub-model, respectively.

[0021] In step S3, the LSSVM prediction model uses a radial basis function (RBF) kernel to establish a nonlinear mapping relationship between laser cutting process parameters and the quality evaluation index values ​​of the cut surface. The RBF kernel is:

[0022] in, and All are input parameters. These are the parameters for the kernel function.

[0023] The fitness function mentioned in step S4 is a weighted sum of the prediction errors of the cutting surface roughness and the kerf perpendicularity, and its expression is:

[0024] in, The fitness value corresponding to the model parameter vector. To predict the root mean square error of the cut surface roughness, The root mean square error for predicting the perpendicularity of the cut is... and These are the weighting coefficients corresponding to the surface roughness and the perpendicularity of the cut, respectively.

[0025] Step S4 uses a chaotic evolutionary algorithm to optimize the model parameters of the LSSVM prediction model, specifically including the following steps: S41: Set the population size for the chaotic evolutionary algorithm Chaotic sampling number Number of maximum fitness evaluations Lower bound of search space and the upper bound of the search space And randomly initialize the population within the search space; S42: Use each individual in the population as a set of LSSVM prediction model parameters, train the LSSVM prediction model separately, and calculate the fitness value of each individual according to the fitness function to determine the current best individual. ; S43: Randomly select two different individuals from the current population. and Treat them as original individuals, and treat two different individuals and By mapping each position to the initial attraction region of the chaotic map, we obtain the initial chaotic position after mapping. and ; S44: with and As the initial value for the chaotic mapping, a two-dimensional discrete chaotic mapping is used to iteratively generate chaotic candidate individuals; S45: Map the chaotic candidate individuals from the chaotic mapping space to the actual search space of the LSSVM prediction model parameters to obtain the actual chaotic candidate parameters; S46: Construct the evolution direction based on the positional difference between the actual chaotic candidate parameters and the original individual, and generate mutated individuals based on the evolution direction; S47: Perform a crossover operation between the mutated individual and the original individual to generate experimental individuals; S48: Compare the fitness values ​​of the experimental individuals with those of the original individuals according to the greedy selection criterion, retain the individuals with better fitness values, and update the current best individual. The process continues until the maximum fitness evaluation count is met or the preset convergence condition is reached, at which point the optimal model parameters of the LSSVM prediction model are output.

[0026] In step S43 above, the two different individuals and The methods for mapping to the initial attraction regions of the chaotic map are as follows:

[0027]

[0028] in, and These are the initial positions of the mapped chaos. and These are two different individuals randomly selected from the current population. and These are the lower bound and upper bound of the search space, respectively; the mapping enables... Located in the interval [-0.5, 0.5], making It lies in the interval [-0.25, 0.25].

[0029] In step S44 above, the initial chaotic position after the above mapping is used. and As the initial value for the two-dimensional discrete chaotic mapping, let ,

[0030] Chaotic candidate individuals are generated iteratively using a two-dimensional discrete chaotic mapping, and the iterative form is as follows:

[0031]

[0032] in, and For the first The chaotic position at the next iteration. and For the first The chaotic position at the next iteration. These are the parameters for controlling chaos. The two-dimensional discrete chaotic mapping generates a non-periodic and ergodic chaotic sequence, which is used to enhance the global search capability of the chaotic evolution algorithm.

[0033] In step S45 above, the method for mapping chaotic candidate individuals from the chaotic mapping space to the actual search space of the LSSVM prediction model parameters is as follows:

[0034]

[0035] in, and These are chaotic candidate individuals in the chaotic mapping space. and These are the actual chaotic candidate parameters after inverse mapping.

[0036] In step S46 above, the evolution direction is constructed based on the positional difference between the actual chaotic candidate parameters and the original individual, and its expression is:

[0037]

[0038] in, and These represent the evolutionary directions corresponding to two different individuals; In step S46 above, the method of generating mutated individuals based on evolutionary direction includes a global exploration mutation method and a local development mutation method, wherein the global exploration mutation method is as follows:

[0039] The local development variation method is as follows:

[0040] in, and For the mutated individual, It is the best individual in the current population. It is a random number or search step size factor in the interval [0, 1]; by randomly selecting the global exploration mutation method or the local development mutation method, the global search and local optimization in the parameter search process of the LSSVM prediction model are realized.

[0041] In step S47 above, the crossover operation is a binomial crossover operation, for the first... Dimensional parameters are used to generate experimental individuals as follows:

[0042] in, For the first individual in the experiment Dimensional parameters, For the mutated individual Dimensional parameters, For the original individual's first Dimensional parameters, For cross control parameters, The dimension index is randomly selected; the crossover control parameter is randomly generated in the interval [0, 1] in each iteration to enhance the diversity of the population search.

[0043] In step S48 above, the greedy selection criterion is: when the fitness value of the experimental individual is less than or equal to the fitness value of the original individual, the experimental individual replaces the original individual; otherwise, the original individual is retained. Its expression is:

[0044] in, For experimental individuals, As the original individual, For the updated individual, and These are the fitness values ​​for the experimental individuals and the original individuals, respectively.

[0045] The beneficial effects of this invention are: This invention combines chaotic evolutionary algorithms with least squares support vector machines to construct a CEO-LSSVM quality prediction model for the laser cutting process of PMMA thick plates. This model effectively establishes a nonlinear mapping relationship between process parameters such as laser power, cutting speed, and defocusing amount, and quality evaluation indicators such as surface roughness and kerf perpendicularity. Compared with traditional methods relying on empirical experiments or single prediction models, this invention utilizes chaotic evolutionary algorithms to optimize the penalty factor and kernel function parameters in the LSSVM prediction model, improving the rationality of model parameter selection and enhancing the model's global search and generalization capabilities. Simultaneously, by standardizing experimental data, the impact of differences in dimensions and numerical ranges on the model training process is reduced, improving the stability and prediction accuracy of model training. This method enables rapid prediction of the quality of laser-cut PMMA thick plates while reducing the number of repeated experiments and material consumption, providing a reliable basis for optimizing laser cutting process parameters, predicting cutting quality, and controlling the processing. Attached Figure Description

[0046] The invention will now be further described with reference to the accompanying drawings.

[0047] Figure 1 This is a flowchart of the method of the present invention; Figure 2 A schematic diagram of the CEO-LSSVM algorithm established in this invention; Figure 3 Comparison of predictions for surface roughness of cut surfaces using different models Figure 1 ; Figure 4 Comparison of predictions for surface roughness of cut surfaces using different models Figure 2 ; Figure 5 Comparison of different models' predictions for cut perpendicularity Figure 1 ; Figure 6Comparison of different models' predictions for cut perpendicularity Figure 2 ; Figure 7 A comparison chart showing the prediction errors of different models for the roughness of the cut surface; Figure 8 This is a comparison chart showing the prediction errors of different models for the perpendicularity of the cut. Detailed Implementation

[0048] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0049] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the specification of this invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0050] The present invention will now be described in detail with reference to the accompanying drawings.

[0051] A method for predicting the quality of laser cutting of thick PMMA plates based on CEO-LSSVM includes the following steps: S1: Collect laser cutting test data for 9mm thick PMMA sheets. The test data includes laser cutting process parameters and cut surface quality evaluation index values. The laser cutting process parameters include laser power, cutting speed, and defocusing amount, which are used as input parameters. The cut surface quality evaluation index values ​​include surface roughness and kerf perpendicularity, which are used as output parameters. Data preprocessing is performed on the collected test data, including outlier removal and missing data supplementation.

[0052] S2: Divide the experimental data into training set and test set, and standardize the training set and test set. Standardization eliminates the impact of differences in the units and numerical ranges of different input parameters on the model training accuracy, resulting in standardized training set and standardized test set.

[0053] S3: Based on the standardized training set, establish an LSSVM prediction model that simultaneously outputs the surface roughness and kerf perpendicularity of the cut surface. The LSSVM prediction model is used to characterize the nonlinear mapping relationship between laser cutting process parameters and the quality evaluation index values ​​of the cut section.

[0054] S4: The Chaotic Evolution Optimization (CEO) algorithm is used to optimize the model parameters of the LSSVM prediction model to obtain the optimal parameter combination. The optimization variable of the CEO algorithm is the LSSVM prediction model parameter vector, which includes a penalty factor and kernel function parameters. The optimal penalty factor and optimal kernel function parameters are obtained through population iterative optimization. The Chaotic Evolution Optimization algorithm uses the prediction error of the standardized training set as the fitness function and aims to minimize the fitness function.

[0055] S5: Substitute the optimal parameter combination of the LSSVM prediction model obtained in step S4 into the LSSVM prediction model to obtain the CEO-LSSVM laser cutting quality prediction model. Then, use the standardized training set to train the CEO-LSSVM laser cutting quality prediction model so that the model learns the nonlinear relationship between the laser cutting process parameters and the quality evaluation index value of the cutting section.

[0056] S6: Input the laser cutting process parameters from the standardized test set into the trained CEO-LSSVM laser cutting quality prediction model, output the corresponding standardized cutting surface roughness prediction value and standardized kerf perpendicularity prediction value, and perform de-standardization on the standardized prediction values ​​(standardized cutting surface roughness prediction value and standardized kerf perpendicularity prediction value) to obtain the cutting surface roughness prediction value and kerf perpendicularity prediction value in actual dimensions; determine whether the CEO-LSSVM laser cutting quality prediction model meets the set model prediction accuracy requirements based on the cutting surface roughness prediction value and kerf perpendicularity prediction value in actual dimensions. If the model prediction accuracy requirements are met, the final CEO-LSSVM laser cutting quality prediction model is obtained; if the model prediction accuracy requirements are not met, re-enter step S4 until the CEO-LSSVM laser cutting quality prediction model meets the set model prediction accuracy requirements.

[0057] The prediction accuracy of the aforementioned model includes the prediction accuracy of the cutting surface roughness, the prediction accuracy of the kerf perpendicularity, and the prediction accuracy of the comprehensive index. Specifically, the prediction accuracy of the cutting surface roughness is calculated by comparing the predicted value of the cutting surface roughness with the actual measured value, and calculating the root mean square error, mean absolute percentage error, and coefficient of determination for both. The prediction accuracy of the kerf perpendicularity is calculated by comparing the predicted value of the kerf perpendicularity with the actual measured value, and calculating the root mean square error, mean absolute percentage error, and coefficient of determination for both. The prediction accuracy of the comprehensive index includes the comprehensive root mean square error, the comprehensive mean absolute percentage error, and the comprehensive coefficient of determination. The comprehensive root mean square error is obtained by weighting the calculated root mean square errors of the cutting surface roughness prediction accuracy and the kerf perpendicularity prediction accuracy, with a preferred weighting factor of 0.5. The comprehensive coefficient of determination is obtained by averaging the sum of the calculated coefficients of determination for the cutting surface roughness prediction accuracy and the kerf perpendicularity prediction accuracy.

[0058] The model prediction accuracy requirements can be set according to actual needs. Thresholds for the root mean square error (RMSE), mean absolute percentage error (MAS), coefficient of determination (CAD), and combined RMSE, MAS, and CAD can be set separately. For example, the CAD and CAD thresholds can both be set to 0.9; the MAS threshold can be set to 5%; and the CAD threshold can be set to 4%. The RMSE and CAD thresholds can be preset based on the actual dimensions of the cutting surface roughness and kerf perpendicularity, as well as the process quality requirements.

[0059] When the calculated root mean square error, mean absolute percentage error, comprehensive root mean square error, and comprehensive mean absolute percentage error are all less than the corresponding set thresholds, and the coefficient of determination threshold and comprehensive coefficient of determination threshold are both greater than the corresponding set thresholds, then the CEO-LSSVM laser cutting quality prediction model meets the set model prediction accuracy requirements. Otherwise, it does not meet the model prediction accuracy requirements, and it is necessary to proceed to step S4 for re-optimization until the requirements are met, and the final CEO-LSSVM laser cutting quality prediction model is obtained.

[0060] During the experiment, the process parameters for laser cutting of thick PMMA plates to be predicted were input into the final CEO-LSSVM laser cutting quality prediction model. Predicted values ​​for the surface roughness and kerf perpendicularity under this parameter combination were obtained. Based on the prediction results, it was determined whether the combination of process parameters met the PMMA thick plate laser cutting section quality evaluation index. After obtaining the predicted values ​​for surface roughness and kerf perpendicularity, these values ​​were compared with preset threshold values ​​for section quality evaluation (surface roughness threshold and kerf perpendicularity threshold). If both predicted values ​​were not greater than the preset threshold values, the current laser cutting process parameters were deemed to meet the PMMA thick plate cutting section quality evaluation index; otherwise, the current laser cutting process parameters were deemed not to meet the section quality evaluation index, and the laser cutting process parameters were readjusted. This provides a basis for optimizing PMMA thick plate laser cutting process parameters, predicting cutting quality, and controlling the processing.

[0061] The experimental equipment used in this embodiment is a 2000W CO2 laser cutting system, mainly composed of a 2000W CO2 laser, a water chiller, a dust removal system, and a three-dimensional five-axis cutting head. PMMA sheets with a thickness between 8-32mm can be referred to as thick PMMA sheets. In this embodiment, the experimental material is a 9mm thick PMMA sheet, and each sample is cut to a size of 50mm. 50mm 9mm.

[0062] The laser cutting test data includes multiple combinations of different laser cutting process parameters and their corresponding cut surface quality evaluation index values. The laser cutting process parameters include laser power, cutting speed, and defocusing amount. The cut surface quality evaluation index values ​​include the surface roughness value and the kerf perpendicularity value, which are obtained through actual measurement during the experiment. In this embodiment, the plate thickness is 9mm, the laser power is 350W~600W, the cutting speed is 12mm / s~22mm / s, and the defocusing amount is -4mm~-9mm. The specific experimental design is shown in Tables 1-4.

[0063] Table 1. Single-factor experimental parameters for laser power

[0064] Table 2 Single-factor experimental parameters for cutting speed

[0065] Table 3. Single-factor experimental parameters for defocusing amount

[0066] Table 4. Orthogonal Experiment Parameter Combination Table

[0067] Based on the single-factor and orthogonal experiments designed in the table, a laser cutting experiment for PMMA was designed. After cutting, the surface roughness and kerf perpendicularity of each group of samples were measured to obtain the surface roughness value and kerf perpendicularity value. The surface roughness Ra and kerf perpendicularity V were selected as the quality evaluation index values ​​for the laser-cut section of thick PMMA plates. The surface roughness Ra characterizes the degree of micro-undulation of the cut section, and the kerf perpendicularity V characterizes the inclination of the cut section along the thickness direction of the plate and the consistency of the upper and lower kerf widths; both are better the smaller they are. The values ​​of the quality evaluation index for the cut section were set to determine whether the laser cutting process parameters meet the quality evaluation index values ​​for the laser-cut section of thick PMMA plates. The values ​​of the quality evaluation index for the cut section include the surface roughness value and the kerf perpendicularity value.

[0068] The experimental data obtained from the above experiments were randomly shuffled and divided into training and testing sets, with 18 sets of data used as the training set and the remaining 9 sets used as the testing set. The laser cutting process parameters (laser power, cutting speed, and defocusing amount) were used as input parameters to the model, while the surface roughness and kerf perpendicularity were used as output parameters to the model.

[0069] Because laser power, cutting speed, defocusing amount, surface roughness, and kerf perpendicularity have different dimensions and numerical ranges, directly inputting them into the LSSVM prediction model for training can easily cause numerical scale differences that affect the model training process. Therefore, before building the LSSVM prediction model, the input and output parameters need to be standardized. The standardization formula is:

[0070] in, The standardized value. This is the original actual value. The mean of the corresponding output parameters in the training set. This represents the standard deviation of the corresponding output parameters in the training set. Standardization maps data of different dimensions to a uniform numerical range, improving the stability and convergence speed of the model training process. For both the training and test sets, the mean of the corresponding variables in the training set is used. and standard deviation Standardization is performed to ensure consistency in data scale during training and testing.

[0071] After the model completes training and outputs prediction results, the standardized predicted values ​​for surface roughness and kerf perpendicularity of the CEO-LSSVM laser cutting quality prediction model are in the standardized space because the output parameters have been standardized. To obtain the cutting quality prediction results in actual dimensions, the standardized prediction values ​​need to be de-standardized. The de-standardization formula is as follows:

[0072] in, The standardized predicted values ​​output by the model. This is the actual predicted value after destandardization. The mean of the corresponding output parameters in the training set. This represents the standard deviation of the output parameters in the training set. Through destandardization, the model output can be restored to predicted values ​​of surface roughness and kerf perpendicularity in actual dimensions, allowing for comparison with actual measurements.

[0073] In this embodiment, a least squares support vector machine (LSSVM) is used to establish a quality prediction model for laser cutting of PMMA thick plates, i.e., the LSSVM prediction model. The LSSVM prediction model can map low-dimensional input parameters to a high-dimensional feature space and establish a quality prediction model in the high-dimensional feature space. It is suitable for laser processing quality prediction problems with small samples, nonlinearity, and multi-parameter coupling.

[0074] For a given training set ,in For input parameters (for the first) (one input sample vector), For output parameters (for the first) The LSSVM prediction model can be expressed as: (the quality evaluation index value of the cut section of each sample).

[0075] in, For the weight vector, It is a nonlinear mapping function. This is a bias term.

[0076] The optimization variables for the LSSVM prediction model are:

[0077] The constraints are:

[0078] in, As a penalty factor, For the first The error term for each sample. The penalty factor is used to balance model complexity and training error, and its value has a significant impact on the model's predictive performance.

[0079] By introducing Lagrange multipliers and solving the problem, the LSSVM prediction model can be expressed as:

[0080] in, For Lagrange multipliers, This is the kernel function.

[0081] In this embodiment, the LSSVM prediction model includes a cutting surface roughness prediction sub-model and a kerf perpendicularity prediction sub-model, which are established respectively. The cutting surface roughness prediction sub-model uses laser power, cutting speed, and defocusing amount as input parameters, and the cutting surface roughness Ra as the output parameter; the kerf perpendicularity prediction sub-model uses laser power, cutting speed, and defocusing amount as input parameters, and the kerf perpendicularity V as the output parameter.

[0082] The parameter vector of the LSSVM prediction model includes a penalty factor. and kernel function parameters Penalty factor in traditional LSSVM models and kernel function parameters Typically, parameter selection relies on manual experience or grid search methods, which suffers from low parameter optimization efficiency, susceptibility to local optima, and unstable model prediction accuracy. To improve the prediction accuracy and generalization ability of the PMMA thick plate laser cutting quality prediction model, this invention employs a chaotic evolutionary algorithm (CEO) to adjust the penalty factor of the LSSVM prediction model. and kernel function parameters Optimize.

[0083] In the LSSVM prediction model, the LSSVM prediction model parameter vector is used as the optimization variable of the chaotic evolution algorithm. The optimization variable can be expressed as:

[0084] When modeling the surface roughness and kerf perpendicularity separately, the optimization variables can be expressed as:

[0085] in, and These are the penalty factor and kernel function parameters of the sub-model for predicting the surface roughness of the cut surface, respectively. and These are the penalty factor and kernel function parameters for the cut perpendicularity prediction sub-model, respectively.

[0086] The CEO algorithm uses minimizing the prediction error on the standardized training set as its optimization objective. In this embodiment, the fitness function is a weighted sum of the prediction errors for the surface roughness and the kerf perpendicularity, and its expression is:

[0087] in, For parameter combination The corresponding fitness value, To predict the root mean square error of the cut surface roughness, The root mean square error for predicting the perpendicularity of the cut is... and These are the weighting coefficients for the surface roughness and the perpendicularity of the cut, respectively. Preferably, and All values ​​are 0.5.

[0088] The CEO algorithm first initializes the population size. Chaotic sampling number Number of maximum fitness evaluations Lower bound of search space and the upper bound of the search space An initial population is randomly generated within the defined parameter search range. Each individual represents a set of LSSVM prediction model parameters. The parameters corresponding to each individual are then... and The data is substituted into the LSSVM prediction model for training, and the fitness value of each individual is calculated based on the fitness function to determine the optimal individual in the current population. .

[0089] During population iteration, two different individuals are randomly selected from the current population. and By mapping each of these regions to the initial attraction region of the chaotic map, we obtain the initial chaotic position after mapping. and Its mapping method is as follows:

[0090]

[0091] in, and These are the lower bound and upper bound of the search space for the optimization variables, respectively.

[0092] With the above-mapped initial chaotic position and As the initial value for the two-dimensional discrete chaotic mapping, let ,

[0093] Chaotic candidate individuals are generated iteratively using a two-dimensional discrete chaotic mapping, and the iterative form is as follows:

[0094]

[0095] in, and For the first The chaotic position at the next iteration. and For the first The chaotic position at the next iteration. These are the parameters for controlling chaos.

[0096] Two-dimensional discrete chaotic mapping can generate chaotic sequences with aperiodicity, ergodicity, and randomness, thereby enhancing the global search capability of the CEO algorithm. The chaotic candidate individuals obtained in the chaotic mapping space are then mapped inversely to the actual search space of the LSSVM parameters to obtain the actual chaotic candidate parameters, whose expression is:

[0097]

[0098] in, and These are chaotic candidate individuals in the chaotic mapping space. and These are the actual chaotic candidate parameters after inverse mapping.

[0099] The evolution direction is constructed based on the positional difference between the actual chaotic candidate parameters and the original individual, and its expression is:

[0100]

[0101] in, and These represent the evolution directions generated by the chaotic candidate parameters.

[0102] The CEO algorithm uses a combination of global exploration and local development to generate mutated individuals during the mutation phase. When using the global exploration method, mutated individuals are generated according to the following formula:

[0103] When using a partial development approach, mutated individuals are generated according to the following formula:

[0104] in, and For the mutated individual, As the current globally optimal individual, It is a random number or search step size factor within the interval [0, 1].

[0105] By randomly selecting a global exploration method or a local development method, the CEO algorithm can expand the search range in the early stage of parameter search, improving the algorithm's ability to escape local optima; and perform local optimization around the current optimal solution in the later stage of parameter search, improving the algorithm's convergence speed and optimization accuracy.

[0106] In the crossover phase, the mutated individuals are crossovered with the original individuals using a binomial method to generate experimental individuals. For the first... The dimension parameter and the method for generating experimental individuals are as follows:

[0107] in, For the first individual in the experiment Dimensional parameters, For the mutated individual Dimensional parameters, For the original individual's first Dimensional parameters, For cross control parameters, The dimension index is randomly selected. The cross control parameters... In each iteration, the population is randomly generated within the interval [0, 1] to improve the diversity of the population search.

[0108] During the selection phase, a greedy selection criterion is used to update the population. When the fitness value of the experimental individual is less than or equal to the fitness value of the original individual, the experimental individual replaces the original individual; otherwise, the original individual is retained. The expression is as follows:

[0109] in, For experimental individuals, As the original individual, For the updated individual, and These are the fitness values ​​for the experimental individuals and the original individuals, respectively.

[0110] Repeatedly perform chaotic mapping, reverse mapping, mutation, crossover, and greedy selection operations until the maximum number of fitness evaluations is reached or the preset convergence condition is met. At this point, the CEO algorithm outputs the optimal individual. And its corresponding parameters are used as the optimal penalty factor for the LSSVM prediction model. and optimal kernel function parameters .

[0111] The optimal penalty factor obtained by the CEO algorithm and optimal kernel function parameters Substituting the values ​​into the LSSVM prediction model, we obtain the CEO-LSSVM laser cutting quality prediction model. The CEO-LSSVM laser cutting quality prediction model is then trained using a training set, enabling the model to learn the nonlinear mapping relationship between laser power, cutting speed, defocusing amount, and the surface roughness and kerf perpendicularity of PMMA thick plate laser cutting.

[0112] The laser cutting process parameters from the standardized test set are input into the trained CEO-LSSVM laser cutting quality prediction model, which outputs the corresponding predicted values ​​for surface roughness and kerf perpendicularity. The predicted surface roughness values ​​are compared with the actual measured values, and the coefficient of determination (R²), root mean square error (RMSE), and mean absolute percentage error (MAPE) are calculated. Similarly, the predicted kerf perpendicularity values ​​are compared with the actual measured values, and the coefficient of determination (R²), root mean square error (RMSE), and mean absolute percentage error (MAPE) are calculated.

[0113] The formula for calculating the coefficient of determination R² is:

[0114] in, For the first The actual measured value of each test sample For the first The predicted value for each test sample. This represents the average of the actual measured values ​​of the test sample. The number of test samples. The closer R² is to 1, the better the model fit.

[0115] The formula for calculating the root mean square error (RMSE) is:

[0116] The smaller the RMSE, the smaller the deviation between the model's predicted value and the actual measured value.

[0117] The formula for calculating the Mean Absolute Percentage Error (MAPE) is:

[0118] The smaller the MAPE, the smaller the proportion of the model prediction error to the actual measurement value, and the higher the model prediction accuracy.

[0119] For the two quality evaluation indicators of the cutting section, surface roughness Ra and kerf perpendicularity V, their corresponding R², RMSE, and MAPE are calculated according to the formulas above. Then, the average of the two R² values ​​for surface roughness Ra and kerf perpendicularity V is used to obtain the comprehensive R² (comprehensive coefficient of determination). The two RMSE values ​​for surface roughness Ra and kerf perpendicularity V are weighted and calculated with a weighting factor of 0.5 to obtain the comprehensive RMSE (comprehensive root mean square error). The two MAPE values ​​for surface roughness Ra and kerf perpendicularity V are weighted and calculated with a weighting factor of 0.5 to obtain the comprehensive MAPE (comprehensive mean absolute percentage error).

[0120] In this embodiment, if the R² of the cutting surface roughness and the perpendicularity of the kerf, and the combined R² are both greater than 0.9, the MAPE of the cutting surface roughness and the perpendicularity of the kerf are both less than 5%, the combined MAPE is less than 4%, and the MAPE and the combined MAPE are less than their respective set thresholds, then the CEO-LSSVM laser cutting quality prediction model is determined to meet the model prediction accuracy requirements. If any of the above conditions are not met, then step S4 is re-entered, the model parameters are readjusted and optimization is performed again until the model prediction accuracy requirements are met, and the final CEO-LSSVM laser cutting quality prediction model is obtained.

[0121] By inputting the process parameters for laser cutting of a 9mm thick PMMA plate into the CEO-LSSVM laser cutting quality prediction model, which ultimately meets the model's prediction accuracy requirements, the corresponding predicted values ​​for surface roughness and kerf perpendicularity can be obtained. Based on the prediction results, it is determined whether the current combination of process parameters meets the PMMA thick plate laser cutting section quality evaluation index values. When both the predicted surface roughness and predicted kerf perpendicularity are less than or equal to the preset section quality evaluation index thresholds (surface roughness threshold and kerf perpendicularity threshold), the current parameter combination is deemed to meet the section quality evaluation index; otherwise, it is deemed not to meet the section quality evaluation index.

[0122] The radial basis function (RBF) neural network, backpropagation (BP) neural network, least squares support vector machine (LSSVM), least squares support vector machine optimized by genetic algorithm (GA-LSSVM), and CEO-LSSVM laser cutting quality prediction model (this invention) were used to predict and analyze the surface roughness and kerf perpendicularity of the test set samples through MATLAB simulation experiments. The experimental results are shown in Tables 5 and 6. 2 RMSE and MAPE represent the prediction accuracy of the prediction model.

[0123] Table 5 Comparison of prediction accuracy of different prediction models for surface roughness of cut surfaces

[0124] Table 6 Comparison of prediction accuracy of different prediction models for cut perpendicularity

[0125] In this embodiment, by append Figure 3 —Appendix Figure 6 It can be seen that different prediction models can reflect the trend of surface roughness and kerf perpendicularity of the cut to a certain extent as the test samples change. Among them, the prediction curve of the CEO-LSSVM laser cutting quality prediction model of the present invention is closer to the true value curve as a whole, indicating that the LSSVM model optimized by the chaotic evolution algorithm can better establish the nonlinear mapping relationship between the laser cutting process parameters and the quality evaluation index value of the cut section.

[0126] To further evaluate the comprehensive predictive ability of each prediction model for the two quality evaluation indicators of the cutting section, namely, surface roughness Ra and kerf perpendicularity V, the comprehensive index prediction accuracy of different models was calculated based on the prediction accuracy evaluation results in Tables 5 and 6. Specifically, the comprehensive RMSE and comprehensive MAPE were obtained by weighting the prediction errors of surface roughness and kerf perpendicularity, respectively, with a weighting coefficient of 0.5 for both. The comprehensive R² was obtained by averaging the R² values ​​corresponding to the two quality evaluation indicators, and the results are shown in Table 7.

[0127] Table 7 Comparison of the dual-index comprehensive prediction performance of different prediction models

[0128] Table 7 shows that the CEO-LSSVM laser cutting quality prediction model has an overall R² of 0.9465, which is higher than the RBF, BP, LSSVM, and GA-LSSVM models; its overall RMSE is 0.0342 and its overall MAPE is 3.15%, both lower than the other comparative models. These results indicate that the CEO-LSSVM laser cutting quality prediction model can not only improve the prediction effect of a single cutting quality index, but also simultaneously reduce the overall prediction error of both surface roughness and kerf perpendicularity.

[0129] Depend on Figure 7 and Figure 8It can be seen that the CEO-LSSVM laser cutting quality prediction model has small prediction errors on most test samples, and the overall error level is low, indicating that the model has good prediction accuracy and stability. It should be noted that the CEO-LSSVM laser cutting quality prediction model does not achieve minimum error on all sample points. This is because the model parameter optimization aims to minimize the overall prediction error, rather than minimizing the error of a single sample. Combining the prediction results and error distribution, it can be concluded that the CEO-LSSVM laser cutting quality prediction model has good predictive ability for the surface roughness and kerf perpendicularity of PMMA thick plate laser cutting.

[0130] In this embodiment, the CEO-LSSVM laser cutting quality prediction model can not only establish a mapping relationship between the laser cutting process parameters of PMMA thick plates and the quality evaluation index values ​​of the cut section based on existing test samples, but also predict the surface roughness and cut perpendicularity of the cut under the new combination of process parameters without conducting actual cutting tests, thereby reducing the number of repeated trial cuts and improving the optimization efficiency of laser cutting process parameters for 9mm PMMA plates.

[0131] In this embodiment of the invention, the PMMA sheet thickness is 9mm. In other embodiments, the method can also be applied to the laser cutting quality prediction of PMMA sheets of other thicknesses or other transparent polymer materials, depending on actual processing requirements.

[0132] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and specification of the present invention.

Claims

1. A method for predicting the quality of laser cutting of thick PMMA plates based on CEO-LSSVM, characterized in that, Includes the following steps: S1: Collect test data for laser cutting of PMMA thick plates. The test data includes laser cutting process parameters and cut surface quality evaluation index values. Among them, the laser cutting process parameters include laser power, cutting speed, and defocusing amount, which are used as input parameters; the cut surface quality evaluation index values ​​include the cutting surface roughness value and the cut perpendicularity value, which are used as output parameters; perform data preprocessing on the collected test data, including outlier data removal and missing data supplementation. S2: Divide the experimental data into training set and test set, and standardize the training set and test set to obtain standardized training set and standardized test set; S3: Based on a standardized training set, establish an LSSVM prediction model that simultaneously outputs the surface roughness and kerf perpendicularity of the cut surface. The LSSVM prediction model is used to characterize the nonlinear mapping relationship between laser cutting process parameters and the quality evaluation index values ​​of the cut section. S4: A chaotic evolutionary algorithm is used to optimize the model parameters of the LSSVM prediction model to obtain the optimal parameter combination of the LSSVM prediction model. The optimization variable of the chaotic evolutionary algorithm is the LSSVM prediction model parameter vector, which includes a penalty factor and kernel function parameters. The optimal penalty factor and optimal kernel function parameters are obtained through population iteration. The chaotic evolutionary algorithm uses the prediction error of the standardized training set as the fitness function and minimizes the fitness function as the optimization objective. S5: Substitute the optimal parameter combination of the LSSVM prediction model obtained in step S4 into the LSSVM prediction model to obtain the CEO-LSSVM laser cutting quality prediction model. Then, use the standardized training set to train the CEO-LSSVM laser cutting quality prediction model so that the model learns the nonlinear relationship between the laser cutting process parameters and the quality evaluation index value of the cutting section. S6: Input the laser cutting process parameters from the standardized test set into the trained CEO-LSSVM laser cutting quality prediction model, output the corresponding standardized cutting surface roughness prediction value and standardized kerf perpendicularity prediction value, and perform de-standardization on the standardized prediction values ​​to obtain the actual dimension cutting surface roughness prediction value and kerf perpendicularity prediction value; determine whether the CEO-LSSVM laser cutting quality prediction model meets the set model prediction accuracy requirements based on the actual dimension cutting surface roughness prediction value and kerf perpendicularity prediction value. If the model prediction accuracy requirements are met, the final CEO-LSSVM laser cutting quality prediction model is obtained; if the model prediction accuracy requirements are not met, return to step S4 until the CEO-LSSVM laser cutting quality prediction model meets the set model prediction accuracy requirements.

2. The method for predicting the quality of PMMA thick plate laser cutting based on CEO-LSSVM according to claim 1, characterized in that, In step S6, the model prediction accuracy includes the prediction accuracy of the cutting surface roughness, the prediction accuracy of the kerf perpendicularity, and the prediction accuracy of the comprehensive index; the prediction accuracy of the cutting surface roughness includes the root mean square error, the mean absolute percentage error, and the coefficient of determination between the predicted value of the cutting surface roughness and the actual measured value of the cutting surface roughness; the prediction accuracy of the kerf perpendicularity includes the root mean square error, the mean absolute percentage error, and the coefficient of determination between the predicted value of the kerf perpendicularity and the actual measured value of the kerf perpendicularity. The comprehensive index prediction accuracy includes the comprehensive root mean square error, the comprehensive average absolute percentage error, and the comprehensive coefficient of determination. The comprehensive root mean square error is obtained by weighting the values ​​of the root mean square error of the predicted accuracy of the cutting surface roughness and the root mean square error of the predicted accuracy of the cut perpendicularity. The overall average absolute percentage error is obtained by weighting the values ​​of the average absolute percentage error of the predicted accuracy of the cut surface roughness and the average absolute percentage error of the predicted accuracy of the cut perpendicularity. The overall determination coefficient is obtained by averaging the sum of the determination coefficients for the predicted accuracy of the cut surface roughness and the predicted accuracy of the cut perpendicularity.

3. The method for predicting the quality of PMMA thick plate laser cutting based on CEO-LSSVM according to claim 1, characterized in that, The LSSVM prediction model includes a sub-model for predicting the surface roughness of the cut surface and a sub-model for predicting the perpendicularity of the cut. The parameter vector of the LSSVM prediction model... Represented as: ； in, and These are the penalty factor and kernel function parameters of the sub-model for predicting the surface roughness of the cut surface, respectively. and These are the penalty factor and kernel function parameters for the cut perpendicularity prediction sub-model, respectively.

4. The method for predicting the quality of PMMA thick plate laser cutting based on CEO-LSSVM according to claim 1, characterized in that, In step S3, the LSSVM prediction model uses a radial basis function to establish a nonlinear mapping relationship between laser cutting process parameters and the quality evaluation index values ​​of the cutting section. The radial basis function is: ； in, and All are input parameters. These are the parameters for the kernel function.

5. The method for predicting the quality of PMMA thick plate laser cutting based on CEO-LSSVM according to claim 1, characterized in that, In step S4, the fitness function is a weighted sum of the prediction errors of the cutting surface roughness and the kerf perpendicularity, and its expression is: ； in, The fitness value corresponding to the model parameter vector. To predict the root mean square error of the cut surface roughness, The root mean square error for predicting the perpendicularity of the cut is... and These are the weighting coefficients corresponding to the surface roughness and the perpendicularity of the cut, respectively.

6. The method for predicting the quality of PMMA thick plate laser cutting based on CEO-LSSVM according to claim 1, characterized in that, Step S4 uses a chaotic evolutionary algorithm to optimize the model parameters of the LSSVM prediction model, specifically including the following steps: S41: Set the population size for the chaotic evolutionary algorithm Chaotic sampling number Number of maximum fitness evaluations Lower bound of search space and the upper bound of the search space And randomly initialize the population within the search space; S42: Use each individual in the population as a set of LSSVM prediction model parameters, train the LSSVM prediction model separately, and calculate the fitness value of each individual according to the fitness function to determine the current best individual. ; S43: Randomly select two different individuals from the current population. and Treat them as original individuals, and treat two different individuals and By mapping each position to the initial attraction region of the chaotic map, we obtain the initial chaotic position after mapping. and ; S44: with and As the initial value for the chaotic mapping, a two-dimensional discrete chaotic mapping is used to iteratively generate chaotic candidate individuals; S45: Map the chaotic candidate individuals from the chaotic mapping space to the actual search space of the LSSVM prediction model parameters to obtain the actual chaotic candidate parameters; S46: Construct the evolution direction based on the positional difference between the actual chaotic candidate parameters and the original individual, and generate mutated individuals based on the evolution direction; S47: Perform a crossover operation between the mutated individual and the original individual to generate experimental individuals; S48: Compare the fitness values ​​of the experimental individuals with those of the original individuals according to the greedy selection criterion, retain the individuals with better fitness values, and update the current best individual. The process continues until the maximum fitness evaluation count is met or the preset convergence condition is reached, at which point the optimal model parameters of the LSSVM prediction model are output.

7. The method for predicting the quality of PMMA thick plate laser cutting based on CEO-LSSVM according to claim 6, characterized in that, In step S43, two different individuals and The methods for mapping to the initial attraction regions of the chaotic map are as follows: ； ； in, and These are the initial positions of the mapped chaos. and These are two different individuals randomly selected from the current population. and These are the lower bound and upper bound of the search space, respectively; the mapping enables... Located in the interval [-0.5, 0.5], making It lies in the interval [-0.25, 0.25].

8. The method for predicting the quality of PMMA thick plate laser cutting based on CEO-LSSVM according to claim 6, characterized in that, In step S44, with and As the initial value for the chaotic mapping, let ， ； Chaotic candidate individuals are generated iteratively using a two-dimensional discrete chaotic mapping, and the iterative form is as follows: ； ； in, and For the first The chaotic position at the next iteration. and For the first The chaotic position at the next iteration. These are the parameters for controlling chaos.

9. The method for predicting the quality of PMMA thick plate laser cutting based on CEO-LSSVM according to claim 6, characterized in that, In step S45, the method for mapping chaotic candidate individuals from the chaotic mapping space to the actual search space of LSSVM prediction model parameters is as follows: ； ； in, and These are chaotic candidate individuals in the chaotic mapping space. and These are the actual chaotic candidate parameters after inverse mapping.

10. The method for predicting the quality of PMMA thick plate laser cutting based on CEO-LSSVM according to claim 6, characterized in that, In step S47, the crossover operation is a binomial crossover operation, for the first... Dimensional parameters are used to generate experimental individuals as follows: ； ； in, For the first individual in the experiment Dimensional parameters, For the mutated individual Dimensional parameters, For the original individual's first Dimensional parameters, For cross control parameters, The dimension index is randomly selected; the crossover control parameter is randomly generated in the interval [0, 1] in each iteration to enhance the diversity of the population search.

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