CF / PEEK milling process parameter optimization method based on improved LSSVR-OOA algorithm

Abstract

The invention relates to a CF / PEEK milling process parameter optimization method based on an improved LSSVR-OOA algorithm, for the acquisition of machining process modeling and process parameter combination, factors in the aspects of process parameters, surface roughness and the like need to be considered, and a plurality of evaluation indexes need to be comprehensively evaluated, so that the process parameters of the CF / PEEK milling process parameter optimization method based on the improved LSSVR-OOA algorithm can be comprehensively evaluated. According to the method, a comprehensive method based on LSSVR and an improved eagle optimization algorithm is adopted, more optimized parameter combinations which can exceed a preset experimental parameter range can be obtained, a multi-objective optimization function is established by using a weight method and serves as a self-adaption function of the eagle optimization algorithm, a model is solved, and the optimal model is obtained. According to the method, the optimized milling process parameter combination is obtained, and the method has better applicability and effectiveness.

Description

Technical Field

[0001] The invention relates to the technical field of production and manufacturing, and in particular to a CF / PEEK milling process parameter optimization method based on an improved LSSVR-OOA algorithm. Background Art

[0002] In recent years, carbon fiber reinforced thermoplastic composites (CFRTPs) have great potential in the fields of aerospace, defense and military, and medical devices due to their high strength-to-weight ratio and corrosion resistance. In recent years, with the increasing requirements for low-cost and high-performance materials, the proportion of CFRTPs in the research and application of composite materials has increased. Carbon fiber reinforced polyetheretherketone (CF / PEEK) composites are typical materials among CFRTPs. They are advanced composite materials composed of carbon fiber as a reinforcement phase and polyetheretherketone as a matrix through a special molding process. Compared with traditional metal materials, CF / PEEK composites exhibit lighter weight, higher strength, higher modulus, high temperature resistance, corrosion resistance, impact wear resistance, and excellent processing performance. Due to the above characteristics, CF / PEEK materials are recognized as high-quality and high-performance materials, which can be used in various fields including aerospace, wind turbine blades, military and new energy vehicles.

[0003] CF / PEEK has good design capabilities, and its components are usually manufactured using a near-net-shape method. After the first molding, secondary processing is usually still required. Milling, as the main processing method for CF / PEEK materials, can meet good geometric accuracy, tolerance levels and edge quality. During the processing, due to the anisotropy and inhomogeneity of the composite material, CF / PEEK is regarded as a difficult-to-process material, and typical surface defects are very likely to occur. Therefore, effectively controlling the surface quality of CF / PEEK processing has become a widely concerned issue and has important practical significance.

[0004] When it comes to process parameter optimization, most scholars focus on metal materials. However, composite materials like CF / PEEK are non-metallic materials and difficult to process. After milling, they face problems such as poor surface quality and high energy consumption. Research on such materials is not yet complete. In terms of modeling, the academic community has established models based on mathematical methods or finite element methods, but research on the use of machine learning methods is not sufficient. In terms of parameter optimization, native optimization algorithms are prone to falling into local optimality and are not suitable for process parameter optimization scenarios, so they need to be improved. Summary of the invention

[0005] The purpose of the present invention is to provide a CF / PEEK milling process parameter optimization method based on an improved LSSVR-OOA algorithm, which can improve the effectiveness of CF / PEEK milling process parameter optimization and has strong applicability.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is: a CF / PEEK milling process parameter optimization method based on an improved LSSVR-OOA algorithm, comprising the following steps:

[0007] Step S1: taking the three-dimensional surface roughness, three-dimensional fractal dimension and milling energy consumption of milling carbon fiber reinforced polyetheretherketone material as optimization targets, and taking cutting speed, feed per tooth, cutting depth and fiber orientation angle as optimization variables, constructing an experimental plan and conducting experiments;

[0008] Step S2: According to the experimental results, the experimental data is processed and a data set is formed, and the data set is divided into a training set D according to a set ratio. t and the test set D v ; Improve the LSSVR algorithm based on multi-kernel learning to obtain the model of evaluation indicators;

[0009] Step S3: Use Tent mapping and convex lens reverse learning strategy to improve the osprey optimization algorithm, increase population diversity, and avoid falling into local optimality;

[0010] Step S4: using the improved Osprey optimization algorithm OOA, taking the test set and the root mean square error RMSE as the fitness function of the OOA algorithm, optimizing the hyperparameter combination of LSSVR, obtaining the optimal hyperparameter combination, and training the LSSVR model; using the entropy weight method to calculate the information entropy value, to assign weights to the three objectives of three-dimensional surface roughness, milling energy consumption, and three-dimensional fractal dimension, and to construct a multi-objective comprehensive evaluation function;

[0011] Step S5: A multi-objective comprehensive evaluation function is used to improve the OOA algorithm to calculate the fitness value, and the improved OOA algorithm is used to optimize the process parameters to obtain the milling parameters corresponding to the optimal carbon fiber polyetheretherketone milling quality, thereby realizing the optimization of CF / PEEK milling process parameters.

[0012] Furthermore, the step S1 includes the following steps:

[0013] S1.1, select cutting speed V c , cutting depth α e and feed per tooth f z For experimental factors, set the level of each factor and design an orthogonal experiment; set the constraints of each factor according to the CF / PEEK milling conditions:

[0014] Cutting speed V min≤V c ≤V max ;

[0015] Cutting depth α min <α e <α max ;

[0016] Feed per tooth f min ≤f z ≤f max ;

[0017] Fiber orientation angles θ1 = 90°, θ2 = 0°;

[0018] Where V min 、V max is the cutting speed V c The minimum and maximum values ​​of α min , α max is the cutting depth α e The minimum and maximum values ​​of f min 、f max is the feed rate f z The minimum and maximum values ​​of θ1 and θ2 are the fiber direction angles;

[0019] S1.2. Conduct milling experiments. After each milling experiment, measure the surface quality of the material after milling, namely the three-dimensional surface roughness and the three-dimensional fractal dimension, to characterize the milling surface quality; and use the electrical parameter signal collected by the electrical signal collector to calculate the milling energy consumption.

[0020] Furthermore, the step S2 comprises the following steps:

[0021] S2.1. After the experiment is completed, the experimental data is processed according to the experimental results, and the data set is set to D = {(x i ,y i )|i=1,2,...n},x i As input variable, y i is the output variable;

[0022] S2.2, preprocess the data to remove outliers in the original data;

[0023] S2.3. Normalize the data so that the output value of each node can vary within a certain range; the normalization equation is:

[0024]

[0025] In the formula, x i Represented as a primitive variable; represents the normalized variable; x maxis the maximum value in the original variable; x min is the minimum value in the original variable;

[0026] The transformed data set is D = {(x i ,y i )|i=1,2,...n};

[0027] S2.4, dividing the processed data into a training set and a test set in a ratio of 8:2; establishing three-dimensional surface roughness, three-dimensional fractal dimension and energy consumption models respectively;

[0028] S2.5. Use Least Squares Support Vector Regression (LSSVR) to segment each training set data and obtain a prediction model for the overall data. The LSSVR algorithm uses nonlinear mapping Map the input space to a high-dimensional feature space and find the optimal linear function in the feature space; construct an improved LSSVR model based on multi-kernel learning, integrate the radial basis kernel function and the polynomial kernel function, and achieve collaborative modeling of local and global features through dynamic optimization of kernel weights to improve the robustness and adaptability of the model;

[0029] First, the prediction function y(x) of LSSVR is expressed as:

[0030]

[0031] In the formula, w represents the weight matrix; represents the nonlinear mapping of the original data into a high-dimensional space; b represents the bias;

[0032] S2.6. Based on the principle of structural risk minimization, the problem of mapping the original data into a high-dimensional space is transformed into a quadratic programming problem:

[0033]

[0034] In the formula, ‖w‖ represents the norm of the weight matrix; γ represents the penalty parameter; e i Represents the true value y i The error between the predicted value y(x), i.e. the deviation variable;

[0035] S2.7. Solve the quadratic programming problem by Lagrange multiplier method:

[0036] The Lagrangian function is defined as:

[0037]

[0038] In the formula, α i represents the Lagrange multiplier;

[0039] S2.8, respectively w, b, αi ,e i Taking the partial derivative and setting it to 0 gives:

[0040]

[0041] Rearrange the above formula to:

[0042]

[0043] Where 1 represents a unit column vector of appropriate dimension, matrix K is the kernel matrix, and y = (y1, y2, …, y n ) T is the vector of target values ​​of the training samples, and I is the unit matrix of appropriate dimension;

[0044] S2.9. Introduce the multi-kernel learning method, combining local kernel functions with global kernel functions, so that the model can maintain good prediction ability when facing different types of data;

[0045] The radial basis kernel function is a local kernel function, and its mathematical expression is:

[0046]

[0047] In the formula, γ1>0 is the kernel parameter, which controls the width of the kernel function, and x i and are two sample vectors in the input dataset;

[0048] The polynomial kernel function is a global kernel function, and its mathematical expression is:

[0049]

[0050] In the formula, α p >0, c p and d are kernel parameters, representing the scaling factor, bias, and order of the polynomial, respectively;

[0051] In order to combine the local characteristics of the radial basis kernel with the global characteristics of the polynomial kernel, a linear combination strategy is used to construct a multi-kernel function:

[0052]

[0053] In the formula, β1, β2 ≥ 0, as weight coefficients, and satisfy β1 + β2 = 1;

[0054] Thus, the improvement of LSSVR algorithm is completed, and its prediction function is expressed as:

[0055]

[0056] The optimization problem solved by the least squares support vector regression algorithm is a convex quadratic programming problem with only one equality constraint, which is suitable for modeling small sample data sets.

[0057] Furthermore, step S3 includes the following steps:

[0058] S3.1. Apply the Tent chaos mapping strategy to the osprey population initialization process to enhance the global search capability, and add the convex lens reverse learning strategy in the development stage to avoid the algorithm from falling into the local optimum, so as to improve the osprey optimization algorithm.

[0059] S3.2, using the improved Osprey optimization algorithm OOA to optimize parameters; set the number of Osprey populations to N, and set the number of iterations to T, set the parameter constraints to be optimized, and initialize the Osprey population to {X i ,i=1,2,...,N}, N represents the size of the osprey population, and the individual osprey is X i ={x i,1 ,x i,2 ,x i,3 ,....,x i,j}, j represents the dimension of the osprey position vector;

[0060] The population is initialized using Tent mapping. First, a series of pseudo-random numbers between the interval [0, 1] are generated using Tent mapping, and then the chaotic sequence is calculated. The Tent mapping formula is as follows:

[0061] Z k =(x z1 ,x z2 ,x z3 ...x zN )

[0062]

[0063] In the formula, Z k+1 represents the chaotic sequence of Tent mapping; N represents the number of individuals in the osprey population; a z is the setting coefficient;

[0064] Map the generated chaotic sequence into the search space of the Osprey optimization algorithm solution:

[0065] x i,j =ld j +(ud j -ld j )×Z k+1

[0066] In the formula, x i,j represents the value of the i-th osprey in the j-th dimension; lb jis the jth dimension to search for the lower bound, ub j is the jth dimension for searching the upper bound;

[0067] S3.3. The osprey hunting process mainly includes two stages. The first stage is that the osprey hunts the fish after detecting its location. For each osprey, the positions of other ospreys with better fitness values ​​in the search space are regarded as "underwater fish schools". If they are not empty, the center position of the "underwater fish school" is calculated; otherwise, the current individual position is retained; the position update formula is set as:

[0068]

[0069] In the formula, P represents the individual set of underwater fish schools; represents the fitness value of the kth osprey; F e j represents the fitness value of the jth osprey; X k represents the position of the kth osprey with better fitness; X best It is the location of the best osprey individuals;

[0070] S3.4. The osprey randomly detects the position of one of the fish and hunts it, and updates the new position of the osprey. The formula is as follows:

[0071]

[0072]

[0073]

[0074] In the formula, is the new position of the ith osprey during the exploration phase The value in the jth dimension; r i,j Represents a random number between the interval [0,1]; SP i is the fish randomly selected by the i-th osprey from its fish swarm P, which is a random number between [0,1]; I i,j The set {1,2} is any number in the set; X i represents the individual position of the i-th osprey, F represents an osprey individual in the exploration phase; ei represents the individual fitness value of the i-th osprey, is the fitness value of the i-th osprey during the exploration phase;

[0075] S3.5, after the osprey kills a fish, it will take it to a suitable location to eat it; this behavior of the osprey causes a slight change in the osprey's position, thereby enhancing the local development ability of the algorithm; the following formula is used to calculate a new random position as the "position suitable for eating fish", and if the fitness value of the new position can be improved, the corresponding osprey's previous position is replaced;

[0076]

[0077]

[0078] Where r is a random number in the interval [0,1]; t is the current number of iterations; T represents the maximum number of iterations required; is the new position of the ith osprey during the exploration phase The value in the jth dimension; X i represents the individual position of the i-th osprey, represents an osprey individual in the exploration phase; is the fitness value of the i-th osprey during the development phase;

[0079] S3.6. During the development phase of the Osprey optimization algorithm, the reverse learning strategy based on the convex lens imaging principle was used to improve the Osprey optimization algorithm. This is an improved strategy that expands the search range by calculating the reverse solution of the current position. The reverse solution of the convex lens imaging reverse learning strategy is calculated using the following formula:

[0080]

[0081] In the formula, represents the inverse solution generated by the convex lens imaging principle; k represents the ratio of the entity height to the imaging height, that is, the telescopic factor;

[0082] The formula for setting the adjustment scaling factor k value is:

[0083] n=(1+(t / T) 1 / 2 ) 10

[0084] Because a smaller k generates a larger range of reverse solutions, while a larger k generates a smaller range of reverse solutions; as the number of iterations increases, the k value will become larger and the range of its reverse solutions will become smaller;

[0085] S3.7. Considering that the reverse solution is not necessarily better than the original solution, a greedy mechanism is introduced to select the individuals after reverse learning to obtain the best individual. The mathematical model formula of the greedy mechanism is as follows:

[0086]

[0087] Where, X new for the selected individuals;

[0088] S3.8, iteratively output the improved osprey optimization algorithm. When the number of iterations is less than the maximum number of iterations T, iterative processing is performed according to steps S3.2 to S3.7; when the iteration termination condition is met, the osprey individual with the best fitness and its fitness value are output, and the value in the position coordinates of the osprey individual is obtained.

[0089] Furthermore, the step S4 comprises the following steps:

[0090] S4.1. The improved Osprey optimization algorithm is used to optimize the LSSVR hyperparameters to ensure the selection of reasonable hyperparameters to improve the performance of the LSSVR algorithm. Model 1, Model 2 and Model 3 are respectively trained and fitted models with the milling process parameter combination as input and the evaluation indicators of three-dimensional surface roughness, milling energy consumption and three-dimensional fractal dimension as output. The data set is divided into training set D t1 , D t2 and D t3 With the test set D v1 , D v2 and D v3 ;

[0091] S4.2. Complete the setting of osprey populations N1, N2, iteration times T1, T2, and least squares support vector regression hyperparameter constraints. The individual position vector of the osprey is determined by the penalty coefficient γ, the kernel parameter γ1 of the radial basis kernel function, and the scaling factor α of the polynomial kernel function. p Composed of test set D v1 , D v2 The root mean square error RMSE is used as the fitness function of the improved Osprey algorithm. The root mean square error RMSE calculation formula is:

[0092]

[0093] In the formula, y i is the measured data; y i (x) is the prediction result of the least squares support vector regression algorithm; N is the number of prediction samples;

[0094] S4.3. Based on the settings of steps S4.1 and S4.2, the hyperparameters of LSSVR are solved through steps S3.2 to S3.8. Then, the hyperparameter combination optimized by the improved Osprey algorithm is used to train the LSSVR models F1, F2 and F3 through steps S2.2 to S2.9.

[0095] Furthermore, the step S5 comprises the following steps:

[0096] S5.1. The entropy weight method is introduced to calculate the model weight ratio, and a multi-objective comprehensive evaluation function is established by this method. For multi-objective optimization, the optimization index values ​​are first preprocessed. To construct a comprehensive evaluation function, the three indicators are set to the same attributes, so the three indicators are converted into cost indicators, as shown below.

[0097]

[0098]

[0099]

[0100] In the formula, Sa min and Sa max is the minimum and maximum value of three-dimensional surface roughness; P min and P max is the minimum and maximum value of milling energy consumption; D min and D max are the minimum and maximum values ​​of the three-dimensional fractal dimension; x represents the optimization variable, i.e., the milling process parameter; and They represent the values ​​of CF / PEEK three-dimensional surface roughness, energy consumption and three-dimensional fractal dimension milling under the current milling process parameters; f1(x), f2(x) and f3(x) represent the values ​​after pretreatment;

[0101] S5.2. Substitute the preprocessed values ​​into the matrix to calculate the prior probability, that is, the proportion of each group of milling process parameters:

[0102]

[0103] In the formula, r ij represents the value of the index after preprocessing, m represents the number of values; R represents the original data matrix after standardization R = (r ij ) m×n ;

[0104] Calculate the proportion of the index value of the i-th item under the j-th index, that is, the prior probability:

[0105]

[0106] In the formula, p ij Indicates the weight of the index value, which means the proportion of the number of samples with the value i in index j to the total number of samples;

[0107] Thus, the weight matrix P of the data is established. ij} m×n ;

[0108] S5.3. The calculation formula of entropy weight is:

[0109]

[0110] In the formula, represents entropy weight, k = 1 / ln(n) > 0, to satisfy

[0111] S5.4. Calculate the information utility value based on entropy weight:

[0112]

[0113] Where, d j represents the information utility value of the jth indicator;

[0114] S5.5. Calculate the weight coefficient of each target by calculating the information utility value;

[0115]

[0116] In the formula, w * j Indicates the weight coefficient of the jth target calculated by the entropy weight method;

[0117] S5.6. Weight each target and establish a comprehensive evaluation function as shown below:

[0118]

[0119] In the formula, F e represents the comprehensive evaluation function established based on the entropy weight method; and They represent the weight coefficients of 3D surface roughness, milling energy consumption and 3D fractal dimension of CF / PEEK milling respectively;

[0120] S5.7. After weighting the three models, a multi-objective comprehensive evaluation function is obtained, which is used as the fitness function of the improved Osprey optimization algorithm:

[0121] minf(x)=F e [f1,f2,f3]

[0122] In the formula, f1, f2, and f3 represent the three-dimensional surface roughness, milling energy consumption, and three-dimensional fractal dimension, respectively;

[0123] S5.8. The improved OOA algorithm is used to optimize the three-dimensional surface roughness, three-dimensional fractal dimension and milling energy consumption of CF / PEEK after milling, and the milling process parameters corresponding to the individual solution at the optimal milling quality are obtained, thereby optimizing the milling process parameters; let the first dimension be the cutting speed V c The second dimension is the cutting depth αe Size, the third dimension is the feed per tooth f z The fourth dimension is the value of the fiber orientation angle θ;

[0124]

[0125] In the formula, x i,1 、x i,2 、x i,3 、x i,4 They represent the values ​​of the four index dimensions of spindle speed, cutting depth, feed per tooth and fiber direction angle of the i-th osprey respectively; x i,1min 、x i,1max Respectively represent the minimum and maximum spindle speed; x i,2min 、x i,2max Respectively represent the minimum and maximum values ​​of cutting depth; x i,3min 、x i,3max They represent the minimum and maximum feed per tooth respectively; u1 and v1 are constants;

[0126] S5.9, perform iterative processing according to steps S3.2 to S3.8; when the iteration termination is satisfied, output the osprey individual with the best fitness and its fitness value to obtain the optimal solution of multi-objective optimization; in the position coordinates of the osprey individual, each dimension is the cutting speed V c , cutting depth α e , feed per tooth f z and fiber orientation angle, and the optimal process parameter combination for multi-objective optimization of CF / PEEK milling was obtained.

[0127] Compared with the prior art, the present invention has the following beneficial effects: the present invention provides a CF / PEEK milling process parameter optimization method based on the improved LSSVR-OOA algorithm. For the modeling of the machining process and the acquisition of process parameter combinations, it is necessary to consider not only factors such as process parameters and surface roughness, but also a comprehensive evaluation of multiple evaluation indicators. Therefore, the method adopts a comprehensive method based on LSSVR and the improved Osprey optimization algorithm, which can obtain more optimized parameter combinations that can exceed the predetermined experimental parameter range, and uses the weighting method to establish a multi-objective optimization function as the adaptability function of the Osprey optimization algorithm. The model is solved to obtain the optimized milling process parameter combination. The method has better applicability and effectiveness. BRIEF DESCRIPTION OF THE DRAWINGS

[0128] Figure 1 It is a flow chart of the method implementation of the embodiment of the present invention. DETAILED DESCRIPTION

[0129] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0130] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0131] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0132] like Figure 1 As shown, this embodiment provides a CF / PEEK milling process parameter optimization method based on the improved LSSVR-OOA algorithm, and its specific implementation steps are as follows.

[0133] Step S1: Taking the three-dimensional surface roughness, three-dimensional fractal dimension and milling energy consumption of milling carbon fiber reinforced polyetheretherketone material as optimization targets, and taking cutting speed, feed per tooth, cutting depth and fiber orientation angle as optimization variables, an experimental plan is constructed and experiments are conducted.

[0134] Step S2: According to the experimental results, the experimental data is processed and formed into a data set, and the data set is divided into a training set D according to a set ratio (8:2) t and the test set D v ; The LSSVR algorithm is improved based on multi-kernel learning to obtain a model of evaluation indicators.

[0135] Step S3: Tent mapping and convex lens reverse learning strategies are used to improve the Osprey optimization algorithm to increase population diversity and avoid falling into local optimality.

[0136] Step S4: Using the improved Osprey optimization algorithm OOA, with the test set and root mean square error RMSE as the fitness function of the OOA algorithm, the hyperparameter combination of LSSVR is optimized to obtain the optimal hyperparameter combination, and the LSSVR model is trained. The information entropy value is calculated by the entropy weight method to assign weights to the three objectives of three-dimensional surface roughness, milling energy consumption and three-dimensional fractal dimension, and a multi-objective comprehensive evaluation function is constructed.

[0137] Step S5: A multi-objective comprehensive evaluation function is used to improve the OOA algorithm to calculate the fitness value, and the improved OOA algorithm is used to optimize the process parameters to obtain the milling parameters corresponding to the optimal carbon fiber polyetheretherketone milling quality, thereby realizing the optimization of CF / PEEK milling process parameters.

[0138] In this embodiment, step S1 includes the following steps:

[0139] S1.1, select cutting speed V c , cutting depth α e and feed per tooth f z For experimental factors, set the level of each factor and design an orthogonal experiment. Set the constraints of each factor according to the CF / PEEK milling conditions:

[0140] Cutting speed V min ≤V c ≤V max ;

[0141] Cutting depth α min <α e <α max ;

[0142] Feed per tooth f min ≤f z ≤f max ;

[0143] Fiber orientation angles θ1 = 90°, θ2 = 0°;

[0144] Where V min 、V max is the cutting speed V c The minimum and maximum values ​​of α min , α max is the cutting depth α e The minimum and maximum values ​​of f min 、f max is the feed rate f z θ1 and θ2 are the minimum and maximum values ​​of the fiber direction angles.

[0145] S1.2. Carry out milling experiments. After each milling experiment, measure the surface quality of the material after milling, namely the three-dimensional surface roughness and three-dimensional fractal dimension, to characterize the milling surface quality. And use the electrical parameter signal collected by the electrical signal collector to calculate the milling energy consumption.

[0146] In this embodiment, step S2 includes the following steps:

[0147] S2.1. After the experiment is completed, the experimental data is processed according to the experimental results, and the data set is set to D = {(x i ,y i )|i=1,2,...n},x i As input variable, y i is the output variable.

[0148] S2.2. The collected data are generally expressed in engineering quantities. Due to certain interference in machine tool processing, there are outliers and noise in the data. It is necessary to preprocess the data to remove the outliers that exist in a very small number of original data.

[0149] S2.3. The scales of various variables may vary greatly, which will have a great impact on the accuracy and stability of numerical calculations. Therefore, before using sample data for training and testing, the data needs to be normalized so that the output value of each node can vary within a certain range. The normalization equation is:

[0150]

[0151] In the formula, x i Represented as a primitive variable; represents the normalized variable; x max is the maximum value in the original variable; x min is the minimum value in the original variable.

[0152] The transformed data set is D = {(x i ,y i )|i=1,2,...n}.

[0153] S2.4. Divide the processed data into training set and test set in a ratio of 8:2 to prepare for subsequent modeling. Establish three-dimensional surface roughness, three-dimensional fractal dimension and energy consumption models respectively.

[0154] S2.5, through the least squares support vector regression (LSSVR) to model each training set data segment to obtain the prediction model of the overall data, LSSVR algorithm through nonlinear mapping The input space is mapped to a high-dimensional feature space, and the optimal linear function is obtained in the feature space; the inner product of the nonlinear mapping is used instead of the direct calculation of the nonlinear mapping, which can significantly simplify the calculation. The traditional LSSVR model may face the problem of a single kernel function selection, thereby limiting the expressive power of the model. The present invention proposes an improved LSSVR model based on multi-kernel learning, which integrates radial basis kernel functions and polynomial kernel functions, and realizes the collaborative modeling of local and global features through dynamic optimization of kernel weights to improve the robustness and adaptability of the model.

[0155] First, the prediction function y(x) of LSSVR can be expressed as:

[0156]

[0157] In the formula, w represents the weight matrix; represents the nonlinear mapping of the original data into a high-dimensional space; b represents the bias.

[0158] S2.6. Based on the principle of structural risk minimization, the problem of mapping the original data into a high-dimensional space is transformed into a quadratic programming problem:

[0159]

[0160] In the formula, ‖w‖ represents the norm of the weight matrix; γ represents the penalty parameter; e i Represents the true value y i The error between the predicted value y(x) and the predicted value y(x), that is, the deviation variable.

[0161] S2.7. Solve the quadratic programming problem by Lagrange multiplier method:

[0162] The Lagrangian function is defined as:

[0163]

[0164] In the formula, α i represents the Lagrange multiplier.

[0165] S2.8, respectively w, b, α i ,e i Taking the partial derivative and setting it to 0 gives:

[0166]

[0167] Rearrange the above formula to:

[0168]

[0169] Where 1 represents a unit column vector of appropriate dimension, matrix K is the kernel matrix, and y = (y1, y2, …, y n ) T is a vector of target values ​​of training samples, and I is a unit matrix of appropriate dimension.

[0170] S2.9. On this basis, a multi-kernel learning method is introduced to effectively improve the generalization performance of LSSVR. By combining local kernel functions with global kernel functions, the model can maintain good predictive ability when facing different types of data.

[0171] The radial basis kernel function is a local kernel function, which is suitable for problems with complex data distribution and significant local characteristics. Its mathematical expression is:

[0172]

[0173] In the formula, γ1>0 is the kernel parameter, which controls the width of the kernel function, and x i and are two sample vectors in the input dataset.

[0174] The polynomial kernel function is a global kernel function that can effectively capture the global nonlinear distribution relationship. Its mathematical expression is:

[0175]

[0176] In the formula, α p >0, c p and d are kernel parameters, representing the scaling factor, bias, and order of the polynomial, respectively.

[0177] In order to combine the local characteristics of the radial basis kernel with the global characteristics of the polynomial kernel, a linear combination strategy is used to construct a multi-kernel function:

[0178]

[0179] In the formula, β1, β2 ≥ 0, as weight coefficients, and satisfy β1 + β2 = 1. It is proposed that β1 = β2 = 0.5 is used for modeling.

[0180] According to the above method, the LSSVR algorithm is improved, and its prediction function can be expressed as:

[0181]

[0182] The optimization problem solved by the least squares support vector regression algorithm is a convex quadratic programming problem with only one equality constraint, which is suitable for modeling small sample data sets.

[0183] In this embodiment, step S3 includes the following steps:

[0184] S3.1. The Tent chaotic mapping strategy is applied to the osprey population initialization process to enhance the global search capability, and a convex lens reverse learning strategy is added in the development stage to prevent the algorithm from falling into the local optimum, so as to complete the improvement of the osprey optimization algorithm.

[0185] S3.2, use the improved Osprey Optimization Algorithm (OOA) to optimize the parameters. Suppose there are N osprey populations, and set the number of iterations to T, set the parameter constraints to be optimized, and initialize the osprey population to {X i ,i=1,2,...,N}, N represents the size of the osprey population, and the individual osprey is X i ={x i,1 ,x i,2 ,x i,3 ,....,x i,j}, j represents the dimension of the osprey position vector.

[0186] In order to make the initial osprey population evenly distributed in the search space, considering that the Tent mapping has good ergodicity, it can effectively avoid the population from being concentrated in a specific area and enhance the global search capability. The population is initialized using the Tent mapping. First, a series of pseudo-random numbers between the interval [0,1] are generated using the Tent mapping, and then the chaotic sequence is calculated. The Tent mapping formula is as follows:

[0187] Z k =(x z1 ,x z2 ,x z3 ...x zN )

[0188]

[0189] In the formula, Z k+1 represents the chaotic sequence of Tent mapping; N represents the number of individuals in the osprey population; a z is the setting coefficient.

[0190] According to experience, generally take a z is 0.4, and the generated chaotic sequence is mapped into the search space of the Osprey optimization algorithm solution:

[0191] x i,j =ld j +(ud j -ld j )×Z k+1

[0192] In the formula, x i,j represents the value of the i-th osprey in the j-th dimension; lb j is the jth dimension to search for the lower bound, ub j is the jth dimension of the search upper bound.

[0193] S3.3. The osprey hunting process mainly includes two stages. The first stage is that the osprey hunts the fish after detecting its location. For each osprey, the positions of other ospreys with better fitness values ​​in the search space are regarded as "underwater fish schools". If they are not empty, the center position of the "underwater fish school" is calculated; otherwise, the current individual position is retained. Set the position update formula as:

[0194]

[0195] In the formula, P represents the individual set of underwater fish schools; represents the fitness value of the kth osprey; represents the fitness value of the jth osprey; X k represents the position of the kth osprey with better fitness; X best It is the location of the best osprey individuals.

[0196] S3.4. The osprey randomly detects the position of one of the fish and hunts it, and updates the new position of the osprey. The formula is as follows:

[0197]

[0198]

[0199]

[0200] In the formula, is the new position of the ith osprey during the exploration phase The value in the jth dimension; r i,j Represents a random number between the interval [0,1]; SP i is the fish randomly selected by the i-th osprey from its fish swarm P, which is a random number between [0,1]; I i,j The set {1,2} is any number in the set; X i represents the individual position of the i-th osprey, F represents an osprey individual in the exploration phase; ei represents the individual fitness value of the i-th osprey, is the fitness value of the i-th osprey in the exploration phase.

[0201] S3.5, After the osprey kills a fish, it will take it to a suitable location to eat it. This behavior of the osprey causes a slight change in the osprey's position, thereby enhancing the local development ability of the algorithm. Use the following formula to calculate a new random position as the "position suitable for eating fish". If the fitness value of the new position can be improved, replace the previous position of the corresponding osprey.

[0202]

[0203]

[0204]

[0205] Where r is a random number in the interval [0,1]; t is the current number of iterations; T represents the maximum number of iterations required; is the new position of the ith osprey during the exploration phase The value in the jth dimension; X i represents the individual position of the i-th osprey, represents an osprey individual in the exploration phase; is the fitness value of the i-th osprey in the development stage.

[0206] S3.6, in the development stage of the Osprey optimization algorithm, the reverse learning strategy based on the convex lens imaging principle is used to improve the Osprey optimization algorithm. This can effectively solve the problem that the reverse learning strategy alone cannot make the individual jump out of the local optimum. It is an improved strategy that expands the search range by calculating the reverse solution of the current position. The reverse solution of the convex lens imaging reverse learning strategy can be calculated by the following formula:

[0207]

[0208] In the formula, represents the inverse solution generated by the convex lens imaging principle; k represents the ratio of the entity height to the imaging height, that is, the scaling factor.

[0209] The formula for setting the adjustment scaling factor k value is:

[0210] n=(1+(t / T) 1 / 2 ) 10

[0211] Because a smaller k generates a larger range of reverse solutions, while a larger k generates a smaller range of reverse solutions. As the number of iterations increases, the k value will become larger and the range of its reverse solutions will become smaller.

[0212] S3.7. Considering that the reverse solution is not necessarily better than the original solution, a greedy mechanism is introduced here to select the individuals after reverse learning, so as to obtain the best individual. The mathematical model formula of the greedy mechanism is as follows:

[0213]

[0214] Where, X new For the selected individuals.

[0215] This mechanism can effectively guide the osprey individuals to the global optimal point, thereby achieving the goal of reverse solution.

[0216] S3.8, iteratively output the improved osprey optimization algorithm. When the number of iterations is less than the maximum number of iterations T, iterative processing is performed according to steps S3.2 to S3.7; when the iteration termination condition is met, the osprey individual with the best fitness and its fitness value are output, and the value in the position coordinates of the osprey individual is obtained.

[0217] In this embodiment, step S4 includes the following steps:

[0218] S4.1. The improved Osprey optimization algorithm is used to optimize the LSSVR hyperparameters to ensure that reasonable hyperparameters are selected to improve the performance of the LSSVR algorithm. Model 1, Model 2, and Model 3 are training fitting models with the combination of milling process parameters as input and the evaluation indicators of three-dimensional surface roughness, milling energy consumption, and three-dimensional fractal dimension as output. The data set is divided into training set D t1 , D t2 and D t3 With the test set D v1 , D v2 and D v3 .

[0219] S4.2. Complete the setting of osprey populations N1, N2, iteration times T1, T2, and least squares support vector regression hyperparameter constraints. The individual position vector of the osprey is determined by the penalty coefficient γ, the kernel parameter γ1 of the radial basis kernel function, and the scaling factor α of the polynomial kernel function. p Composed of test set D v1 , D v2 The root mean square error RMSE is used as the fitness function of the improved Osprey algorithm. The root mean square error RMSE calculation formula is:

[0220]

[0221] In the formula, y i is the measured data; y i (x) is the prediction result of the least squares support vector regression algorithm; N is the number of prediction samples;

[0222] S4.3. Based on the settings of steps S4.1 and S4.2, the hyperparameters of LSSVR are solved through steps S3.2 to S3.8. Then, the hyperparameter combination optimized by the improved Osprey algorithm is used to train the LSSVR models F1, F2 and F3 through steps S2.2 to S2.9.

[0223] In this embodiment, step S5 includes the following steps:

[0224] S5.1. The entropy weight method is introduced to calculate the model weight ratio. Entropy is a measure of the degree of chaos. The present invention adopts this method to establish a multi-objective comprehensive evaluation function. For multi-objective optimization, it is necessary to first pre-process the optimization index values. Among the indicators, the three-dimensional surface roughness and milling energy consumption are cost-type indicators, and the smaller the value, the better; while for the three-dimensional fractal dimension, it is an economic indicator, and the larger the value, the better. In order to construct a comprehensive evaluation function, the three indicators need to be set to the same attributes, so the three indicators are converted into cost-type indicators, as shown below.

[0225]

[0226]

[0227]

[0228] In the formula, Sa min and Sa max is the minimum and maximum value of three-dimensional surface roughness; P min and P max is the minimum and maximum value of milling energy consumption; D min and D max are the minimum and maximum values ​​of the three-dimensional fractal dimension; x represents the optimization variable, i.e., the milling process parameter; and They represent the values ​​of 3D surface roughness, energy consumption and 3D fractal dimension of CF / PEEK under the current milling process parameters; f1(x), f2(x) and f3(x) represent the values ​​after preprocessing.

[0229] S5.2. Substitute the preprocessed values ​​into the matrix to calculate the prior probability, that is, the proportion of each group of milling process parameters:

[0230]

[0231] In the formula, r ij represents the value of the index after preprocessing, m represents the number of values; R represents the original data matrix after standardization R = (r ij ) m×n .

[0232] Calculate the proportion (prior probability) of the index value of the i-th item under the j-th index:

[0233]

[0234] In the formula, p ij It represents the weight of the index value (prior probability), which means the proportion of the number of samples with value i in index j to the total number of samples.

[0235] Thus, the weight matrix P of the data can be established. ij} m×n .

[0236] S5.3. The calculation formula of entropy weight is:

[0237]

[0238] In the formula, represents entropy weight, k = 1 / ln(n) > 0, to satisfy

[0239] S5.4. Calculate the information utility value based on entropy weight:

[0240]

[0241] Where, d j Represents the information utility value of the j-th indicator.

[0242] The information utility value of an indicator depends on the information entropy e of the indicator. j The difference between 1 and 1 directly affects the size of the weight. The larger the information utility value, the greater its importance to the evaluation and the greater the weight.

[0243] S5.5. Calculate the value of information utility and then calculate the weight coefficient of each target.

[0244]

[0245] In the formula, w * j It indicates the weight coefficient of the j-th target calculated by the entropy weight method.

[0246] S5.6. Weight each target and establish a comprehensive evaluation function as shown below:

[0247]

[0248] In the formula, F e represents the comprehensive evaluation function established based on the entropy weight method; and They represent the weight coefficients of CF / PEEK milling three-dimensional surface roughness, milling energy consumption and three-dimensional fractal dimension respectively.

[0249] S5.7. After weighting the three models, a multi-objective comprehensive evaluation function is obtained, which is used as the fitness function of the improved Osprey optimization algorithm:

[0250] minf(x)=F e [f1,f2,f3]

[0251] Where f1, f2, and f3 represent the three-dimensional surface roughness, milling energy consumption, and three-dimensional fractal dimension, respectively.

[0252] S5.8. The improved OOA algorithm is used to optimize the three-dimensional surface roughness, three-dimensional fractal dimension and milling energy consumption of CF / PEEK after milling, and the milling process parameters corresponding to the individual solution at the optimal milling quality are obtained, thereby optimizing the milling process parameters. Let the first dimension be the cutting speed V c The second dimension is the cutting depth α e Size, the third dimension is the feed per tooth f z The fourth dimension is the value of the fiber orientation angle θ.

[0253]

[0254] In the formula, x i,1 、x i,2 、x i,3 、x i,4 They represent the values ​​of the four index dimensions of spindle speed, cutting depth, feed per tooth and fiber direction angle of the i-th osprey respectively; x i,1min 、x i,1max Respectively represent the minimum and maximum spindle speed; x i,2min 、x i,2max Respectively represent the minimum and maximum values ​​of cutting depth; x i,3min 、x i,3max They represent the minimum and maximum feed per tooth respectively; u1 and v1 are constants.

[0255] S5.9, perform iterative processing according to steps S3.2 to S3.8; when the iteration termination is satisfied, output the osprey individual with the best fitness and its fitness value to obtain the optimal solution of multi-objective optimization; in the position coordinates of the osprey individual, each dimension is the cutting speed V c , cutting depth α e , feed per tooth f z and fiber orientation angle, and the optimal process parameter combination for multi-objective optimization of CF / PEEK milling was obtained.

[0256] This embodiment uses the VMC vertical machining center of Shenyang Machine Tool Plant for processing, with a maximum speed of 10000rpm and an XYZ axis positioning accuracy of 0.01mm. A 10mm single-edged carbide tool is selected as the milling tool, and the material is a CF / PEEK layer with a fixed fiber orientation and a size of 100mm*100mm. In the milling CF / PEEK material experiment, the key process parameters include cutting speed, cutting depth, feed per tooth and fiber orientation angle. The orthogonal test method is used to design the experiment based on the determined factors and levels, and a mixed level orthogonal experiment is designed, with a total of 16 groups, as shown in Table 1 and Table 2.

[0257] Table 1 Factors and level settings

[0258]

[0259] Table 2 Hybrid orthogonal experiment planning

[0260]

[0261]

[0262] According to the experimental arrangement in Table 2, the CF / PEEK laminate with a size of 100mm*100mm is milled. After the experiment, the three-dimensional surface roughness, milling energy consumption and three-dimensional fractal dimension of the quality evaluation indicators after cutting need to be measured and calculated. First, use a three-dimensional surface profile measuring instrument to calculate the three-dimensional surface roughness; use an intelligent collector to collect electrical signals during the milling process and record the energy consumption required during the processing; use a scanning electron microscope to observe and measure the plane after the test, and calculate the three-dimensional fractal dimension. The method for obtaining data is: after milling based on a set of process parameters, measure the three-dimensional surface roughness, calculate the three-dimensional fractal dimension, complete three times and take the average value. Table 3 gives the data of the titanium alloy milling experiment.

[0263] Table 3 CF / PEEK milling experimental data results

[0264]

[0265] (1) Hyperparameter Optimization of Least Squares Support Vector Regression Model

[0266] Before training the least squares support vector regression model, it is necessary to adjust the penalty coefficient γ, the kernel parameter γ1 of the radial basis kernel function, and the scaling factor α of the polynomial kernel function. p Hyperparameter optimization, polynomial kernel function bias c p =1 and the polynomial order d=2 are set as default values ​​and do not participate in the optimization. In view of the instability of manual parameter adjustment, the effect of parameter adjustment is overly dependent on the experience of the parameter adjuster, so the LSSVR hyperparameters of the present invention use the osprey algorithm to adjust the parameters, and use the optimized hyperparameters to train the model of the evaluation index. Set the osprey individual position vector to consist of hyperparameters, set the number of osprey populations N1, N2, N3 = 100, the number of iterations T1, T2, T3 = 50, and the hyperparameter constraints are set to the formula:

[0267]

[0268] After optimization by OOA algorithm, the optimal hyperparameter combination of three-dimensional surface roughness, milling energy consumption and three-dimensional fractal dimension fitting model was obtained, and the LSSVR1 model, LSSVR2 model and LSSVR3 model were obtained.

[0269] (2) Establishment of multi-objective comprehensive evaluation function

[0270] The weight coefficients of the three-dimensional surface roughness, milling energy consumption and three-dimensional fractal dimension calculated by steps S5.1 to S5.6 are 0.4716, 0.2812 and 0.2472 respectively. Combined with the established fitting model, the multi-objective comprehensive evaluation function formula is constructed:

[0271] F e(f1,f2,f3)=0.4716f1(x)+0.2812f2(x)+0.2472f3(x)

[0272] (3) Improve the parameter settings of the Osprey optimization algorithm

[0273] Use the constructed multi-objective comprehensive evaluation function as the fitness function of the improved osprey optimization algorithm and set the osprey population size N x =100 iterations T X =50=, the position of the osprey is X i ={x i,1 ,x i,2 ,x i,3 ,x i,4}, the fitness function is set to: minf(x) = F e [f1,f2,f3], the milling process parameter constraints are defined as:

[0274]

[0275] Iterate to obtain the optimal osprey individual solution vector.

[0276] (4) Optimization results of the Osprey algorithm are not improved

[0277] Table 4 shows the process parameter combinations obtained by the unimproved LSSVR-OOA Osprey optimization algorithm. After the iteration is terminated, the CF / PEEK milling process parameter combinations are shown in Table 4.

[0278] Table 4 Multi-objective optimization results of milling process parameters after optimization by unmodified LSSVR-OOA algorithm

[0279]

[0280] The experimental results of three-dimensional surface roughness, milling energy consumption and three-dimensional fractal dimension obtained by the CF / PEEK milling experiment based on this parameter combination are shown in Table 5.

[0281] Table 5 Milling experimental results of process parameters obtained by optimizing the LSSVR-OOA algorithm without improvement

[0282]

[0283] (5) Improved Osprey algorithm optimization results

[0284] Table 6 shows the process parameter combinations obtained by the improved LSSVR-OOA Osprey optimization algorithm, as shown in Table 6

[0285] Table 6 Milling process parameter optimization results

[0286]

[0287] The experimental results of three-dimensional surface roughness, milling energy consumption and three-dimensional fractal dimension obtained by the CF / PEEK milling experiment based on this parameter combination are shown in Table 7.

[0288] Table 7 Milling experimental results of process parameters obtained by optimizing the improved LSSVR-OOA algorithm

[0289]

[0290] After comparison, the experimental results of the milling process parameters optimized by the improved LSSVR-OOA algorithm showed that the three-dimensional surface roughness, milling energy consumption and three-dimensional fractal dimension were significantly improved.

[0291] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0292] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0293] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0294] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0295] The above is only a preferred embodiment of the present invention, and does not limit the present invention in other forms. Any technician familiar with the profession may use the above disclosed technical content to change or modify it into an equivalent embodiment with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.

Claims

1. A CF / PEEK milling process parameter optimization method based on improved LSSVR-OOA algorithm, characterized in that: The following steps are involved: Step S1: taking the three-dimensional surface roughness, three-dimensional fractal dimension and milling energy consumption of milling carbon fiber reinforced polyetheretherketone material as optimization targets, and taking cutting speed, feed per tooth, cutting depth and fiber orientation angle as optimization variables, constructing an experimental plan and conducting experiments; Step S2: According to the experimental results, the experimental data is processed and a data set is formed, and the data set is divided into training set D and training set D according to the set ratio. t and the test set D v ; Improve the LSSVR algorithm based on multi-kernel learning to obtain the model of evaluation indicators; Step S3: Use Tent mapping and convex lens reverse learning strategy to improve the osprey optimization algorithm, increase population diversity, and avoid falling into local optimality; Step S4: using the improved Osprey optimization algorithm OOA, taking the test set and the root mean square error RMSE as the fitness function of the OOA algorithm, optimizing the hyperparameter combination of LSSVR, obtaining the optimal hyperparameter combination, and training the LSSVR model; using the entropy weight method to calculate the information entropy value, to assign weights to the three objectives of three-dimensional surface roughness, milling energy consumption, and three-dimensional fractal dimension, and to construct a multi-objective comprehensive evaluation function; Step S5: A multi-objective comprehensive evaluation function is used to improve the OOA algorithm to calculate the fitness value, and the improved OOA algorithm is used to optimize the process parameters to obtain the milling parameters corresponding to the optimal carbon fiber polyetheretherketone milling quality, thereby realizing the optimization of CF / PEEK milling process parameters.

2. The CF / PEEK milling process parameter optimization method based on the improved LSSVR-OOA algorithm according to claim 1 is characterized in that: The step S1 comprises the following steps: S1.1, Select cutting speed V c , cutting depth α e and feed per tooth f z For experimental factors, set the level of each factor and design an orthogonal experiment; set the constraints of each factor according to the CF / PEEK milling conditions: Cutting speed V min ≤V c ≤V max ; Cutting depth α min <α e <α max ; Feed per tooth f min ≤f z ≤f max ; Fiber orientation angles θ1 = 90°, θ2 = 0°; Where V min 、V max is the cutting speed V c The minimum and maximum values ​​of α min , α max is the cutting depth α e The minimum and maximum values ​​of f min 、f max is the feed rate f z The minimum and maximum values ​​of θ1 and θ2 are the fiber direction angles; S1.

2. Conduct milling experiments. After each milling experiment, measure the surface quality of the material after milling, namely the three-dimensional surface roughness and the three-dimensional fractal dimension, to characterize the milling surface quality; and use the electrical parameter signal collected by the electrical signal collector to calculate the milling energy consumption.

3. The CF / PEEK milling process parameter optimization method based on the improved LSSVR-OOA algorithm according to claim 1 is characterized in that: The step S2 comprises the following steps: S2.

1. After the experiment is completed, the experimental data is processed according to the experimental results, and the data set is set to D = {(x i ,y i )|i=1,2,...n},x i As input variable, y i is the output variable; S2.2, preprocess the data to remove outliers in the original data; S2.

3. Normalize the data so that the output value of each node can vary within a certain range; the normalization equation is: In the formula, x i Represented as a primitive variable; represents the normalized variable; x max is the maximum value in the original variable; x min is the minimum value in the original variable; The transformed data set is D = {(x i ,y i )|i=1,2,...n}; S2.4, dividing the processed data into a training set and a test set in a ratio of 8:2; establishing three-dimensional surface roughness, three-dimensional fractal dimension and energy consumption models respectively; S2.

5. Use Least Squares Support Vector Regression (LSSVR) to segment each training set data and obtain a prediction model for the overall data. The LSSVR algorithm uses nonlinear mapping Map the input space to a high-dimensional feature space and find the optimal linear function in the feature space; construct an improved LSSVR model based on multi-kernel learning, integrate the radial basis kernel function and the polynomial kernel function, and achieve collaborative modeling of local and global features through dynamic optimization of kernel weights to improve the robustness and adaptability of the model; First, the prediction function y(x) of LSSVR is expressed as: In the formula, w represents the weight matrix; represents the nonlinear mapping of the original data into a high-dimensional space; b represents the bias; S2.

6. Based on the principle of structural risk minimization, the problem of mapping the original data into a high-dimensional space is transformed into a quadratic programming problem: In the formula, ‖w‖ represents the norm of the weight matrix; γ represents the penalty parameter; e i Represents the true value y i The error between the predicted value y(x), i.e. the deviation variable; S2.

7. Solve the quadratic programming problem by Lagrange multiplier method: The Lagrangian function is defined as: In the formula, α i represents the Lagrange multiplier; S2.8, respectively w, b, α i ,e i Taking the partial derivative and setting it to 0 gives: Rearrange the above formula to: Where 1 represents a unit column vector of appropriate dimension, matrix K is the kernel matrix, and y = (y1, y2, …, y n ) T is the vector of target values ​​of the training samples, and I is the unit matrix of appropriate dimension; S2.

9. Introduce the multi-kernel learning method, combining local kernel functions with global kernel functions, so that the model can maintain good prediction ability when facing different types of data; The radial basis kernel function is a local kernel function, and its mathematical expression is: In the formula, γ1>0 is the kernel parameter, which controls the width of the kernel function, and x i and are two sample vectors in the input dataset; The polynomial kernel function is a global kernel function, and its mathematical expression is: In the formula, α p >0, c p and d are kernel parameters, representing the scaling factor, bias, and order of the polynomial, respectively; In order to combine the local characteristics of the radial basis kernel with the global characteristics of the polynomial kernel, a linear combination strategy is used to construct a multi-kernel function: In the formula, β1, β2 ≥ 0, as weight coefficients, and satisfy β1 + β2 = 1; Thus, the improvement of LSSVR algorithm is completed, and its prediction function is expressed as: The optimization problem solved by the least squares support vector regression algorithm is a convex quadratic programming problem with only one equality constraint, which is suitable for modeling small sample data sets.

4. The CF / PEEK milling process parameter optimization method based on the improved LSSVR-OOA algorithm according to claim 3 is characterized in that: The step S3 comprises the following steps: S3.

1. Apply the Tent chaos mapping strategy to the osprey population initialization process to enhance the global search capability, and add the convex lens reverse learning strategy in the development stage to avoid the algorithm from falling into the local optimum, so as to improve the osprey optimization algorithm. S3.2, using the improved Osprey optimization algorithm OOA to optimize parameters; set the number of Osprey populations to N, and set the number of iterations to T, set the parameter constraints to be optimized, and initialize the Osprey population to {X i ,i=1,2,...,N}, N represents the size of the osprey population, and the individual osprey is X i ={x i,1 ,x i,2 ,x i,3 ,....,x i,j }, j represents the dimension of the osprey position vector; The population is initialized using Tent mapping. First, a series of pseudo-random numbers between the interval [0, 1] are generated using Tent mapping, and then the chaotic sequence is calculated. The Tent mapping formula is as follows: Z k =(x z1 ,x z2 ,x z3 ...x zN ) In the formula, Z k+1 represents the chaotic sequence of Tent mapping; N represents the number of individuals in the osprey population; a z is the setting coefficient; Map the generated chaotic sequence into the search space of the Osprey optimization algorithm solution: x i,j =old j +(out j -ld j )×Z k+1 In the formula, x i,j represents the value of the i-th osprey in the j-th dimension; lb j is the jth dimension to search for the lower bound, ub j is the jth dimension for searching the upper bound; S3.

3. The osprey hunting process mainly includes two stages. The first stage is that the osprey hunts the fish after detecting its location. For each osprey, the positions of other ospreys with better fitness values ​​in the search space are regarded as "underwater fish schools". If they are not empty, the center position of the "underwater fish school" is calculated; otherwise, the current individual position is retained; the position update formula is set as: In the formula, P represents the individual set of underwater fish schools; represents the fitness value of the kth osprey; F e j represents the fitness value of the jth osprey; X k represents the position of the kth osprey with better fitness; X best It is the location of the best osprey individuals; S3.

4. The osprey randomly detects the position of one of the fish and hunts it, and updates the new position of the osprey. The formula is as follows: In the formula, is the new position of the ith osprey during the exploration phase The value in the jth dimension; r i,j Represents a random number between the interval [0,1]; SP i is the fish randomly selected by the i-th osprey from its fish swarm P, which is a random number between [0,1]; I i,j The set {1,2} is any number in the set; X i represents the individual position of the i-th osprey, F represents an osprey individual in the exploration phase; ei represents the individual fitness value of the i-th osprey, is the fitness value of the i-th osprey during the exploration phase; S3.5, after the osprey kills a fish, it will take it to a suitable location to eat it; this behavior of the osprey causes a slight change in the osprey's position, thereby enhancing the local development ability of the algorithm; the following formula is used to calculate a new random position as the "position suitable for eating fish", and if the fitness value of the new position can be improved, the corresponding osprey's previous position is replaced; Where r is a random number in the interval [0,1]; t is the current number of iterations; T represents the maximum number of iterations required; is the new position of the ith osprey during the exploration phase The value in the jth dimension; X i represents the individual position of the i-th osprey, represents an individual osprey in the exploration phase; is the fitness value of the i-th osprey during the development phase; S3.

6. During the development phase of the Osprey optimization algorithm, the reverse learning strategy based on the convex lens imaging principle was used to improve the Osprey optimization algorithm. This is an improved strategy that expands the search range by calculating the reverse solution of the current position. The reverse solution of the convex lens imaging reverse learning strategy is calculated using the following formula: In the formula, represents the inverse solution generated by the convex lens imaging principle; k represents the ratio of the entity height to the imaging height, that is, the telescopic factor; The formula for setting the adjustment scaling factor k value is: n=(1+(t / T) 1 / 2 ) 10 Because a smaller k generates a larger range of reverse solutions, while a larger k generates a smaller range of reverse solutions; as the number of iterations increases, the k value will become larger and the range of its reverse solutions will become smaller; S3.

7. Considering that the reverse solution is not necessarily better than the original solution, a greedy mechanism is introduced to select the individuals after reverse learning to obtain the best individual. The mathematical model formula of the greedy mechanism is as follows: Where, X new For the selected individuals; S3.8, iteratively output the improved osprey optimization algorithm. When the number of iterations is less than the maximum number of iterations T, iterative processing is performed according to steps S3.2 to S3.7; when the iteration termination condition is met, the osprey individual with the best fitness and its fitness value are output, and the value in the position coordinates of the osprey individual is obtained.

5. The CF / PEEK milling process parameter optimization method based on the improved LSSVR-OOA algorithm according to claim 4 is characterized in that: The step S4 comprises the following steps: S4.

1. The improved Osprey optimization algorithm is used to optimize the LSSVR hyperparameters to ensure the selection of reasonable hyperparameters to improve the performance of the LSSVR algorithm. Model 1, Model 2 and Model 3 are respectively trained and fitted models with the milling process parameter combination as input and the evaluation indicators of three-dimensional surface roughness, milling energy consumption and three-dimensional fractal dimension as output. The data set is divided into training set D t1 , D t2 and D t3 With the test set D v1 , D v2 and D v3 ; S4.

2. Complete the setting of osprey populations N1, N2, iteration times T1, T2, and least squares support vector regression hyperparameter constraints. The individual position vector of the osprey is determined by the penalty coefficient γ, the kernel parameter γ1 of the radial basis kernel function, and the scaling factor α of the polynomial kernel function. p Composed of test set D v1 , D v2 The root mean square error RMSE is used as the fitness function of the improved Osprey algorithm. The root mean square error RMSE calculation formula is: In the formula, y i is the measured data; y i (x) is the prediction result of the least squares support vector regression algorithm; N is the number of prediction samples; S4.

3. Based on the settings of steps S4.1 and S4.2, the hyperparameters of LSSVR are solved through steps S3.2 to S3.

8. Then, the hyperparameter combination optimized by the improved Osprey algorithm is used to train the LSSVR models F1, F2 and F3 through steps S2.2 to S2.

9.

6. The CF / PEEK milling process parameter optimization method based on the improved LSSVR-OOA algorithm according to claim 5, characterized in that: The step S5 comprises the following steps: S5.

1. The entropy weight method is introduced to calculate the model weight ratio, and a multi-objective comprehensive evaluation function is established by this method. For multi-objective optimization, the optimization index values ​​are first preprocessed. To construct a comprehensive evaluation function, the three indicators are set to the same attributes, so the three indicators are converted into cost indicators, as shown below. In the formula, Sa min and Sa max is the minimum and maximum value of three-dimensional surface roughness; P min and P max is the minimum and maximum value of milling energy consumption; D min and D max are the minimum and maximum values ​​of the three-dimensional fractal dimension; x represents the optimization variable, i.e., the milling process parameter; and They represent the values ​​of CF / PEEK three-dimensional surface roughness, energy consumption and three-dimensional fractal dimension milling under the current milling process parameters; f1(x), f2(x) and f3(x) represent the values ​​after pretreatment; S5.

2. Substitute the preprocessed values ​​into the matrix to calculate the prior probability, that is, the proportion of each group of milling process parameters: In the formula, r ij represents the value of the index after preprocessing, m represents the number of values; R represents the original data matrix after standardization R = (r ij ) m×n ; Calculate the proportion of the index value of the i-th item under the j-th index, that is, the prior probability: In the formula, p ij Indicates the weight of the index value, which means the proportion of the number of samples with the value i in index j to the total number of samples; Thus, the weight matrix P of the data is established. ij } m×n ; S5.

3. The calculation formula of entropy weight is: In the formula, represents entropy weight, k = 1 / ln(n) > 0, to satisfy S5.

4. Calculate the information utility value based on entropy weight: Where, d j represents the information utility value of the jth indicator; S5.

5. Calculate the weight coefficient of each target by calculating the information utility value; In the formula, w * j Indicates the weight coefficient of the jth target calculated by the entropy weight method; S5.

6. Weight each target and establish a comprehensive evaluation function as shown below: In the formula, F e represents the comprehensive evaluation function established based on the entropy weight method; and They represent the weight coefficients of 3D surface roughness, milling energy consumption and 3D fractal dimension of CF / PEEK milling respectively; S5.

7. After weighting the three models, a multi-objective comprehensive evaluation function is obtained, which is used as the fitness function of the improved Osprey optimization algorithm: <h2 style=";text-align:left;direction:ltr">minf(x) = F<h2 style=";text-align:left;direction:ltr"> e <h2 style=";text-align:left;direction:ltr"> [f1,f2,f3] In the formula, f1, f2, and f3 represent the three-dimensional surface roughness, milling energy consumption, and three-dimensional fractal dimension, respectively; S5.

8. The improved OOA algorithm is used to optimize the three-dimensional surface roughness, three-dimensional fractal dimension and milling energy consumption of CF / PEEK after milling, and the milling process parameters corresponding to the individual solution at the optimal milling quality are obtained, thereby optimizing the milling process parameters; let the first dimension be the cutting speed V c The second dimension is the cutting depth α e Size, the third dimension is the feed per tooth f z The fourth dimension is the value of the fiber orientation angle θ; In the formula, x i,1 、x i,2 、x i,3 、x i,4 They represent the values ​​of the spindle speed, cutting depth, feed per tooth and fiber direction angle of the i-th osprey respectively; x i,1min 、x i,1max Respectively represent the minimum and maximum spindle speed; x i,2min 、x i,2max Respectively represent the minimum and maximum values ​​of cutting depth; x i,3min 、x i,3max They represent the minimum and maximum feed per tooth respectively; u1 and v1 are constants; S5.9, perform iterative processing according to steps S3.2 to S3.8; when the iteration termination is satisfied, output the osprey individual with the best fitness and its fitness value to obtain the optimal solution of multi-objective optimization; in the position coordinates of the osprey individual, each dimension is the cutting speed V c , cutting depth α e , feed per tooth f z and fiber orientation angle, and the optimal process parameter combination for multi-objective optimization of CF / PEEK milling was obtained.

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