A prediction method for surface roughness of milling workpiece

Abstract

The present invention relates to a method for predicting the surface roughness of a milled workpiece, comprising the following steps: determining the topological structure of a BP neural network; performing normalization processing on input data and output data; determining the number of weights and thresholds required for optimization by the BP neural network; setting the scale and number of iterations of a northern goshawk to form a northern goshawk population position matrix; and using the error function between the predicted value and the measured value as a fitness function. F The fitness value of the northern goshawk's position is calculated; the northern goshawk position with the minimum fitness value is the prey location; the northern goshawk position is updated and the prey location is re-determined using the prey recognition model; the prey location is updated using the prey pursuit and prey escape models to obtain optimized weights and thresholds; the optimized weights and thresholds are substituted into the BP neural network structure for training, and the surface roughness of the workpiece under different working conditions is ultimately predicted based on the training results. The present invention enhances the prediction capability and prediction accuracy of the neural network and improves the calculation speed.

Description

Technical Field

[0001] The present invention relates to the field of milling processing, and in particular to a method for predicting the surface roughness of a milled workpiece. Background Art

[0002] With the rapid development of the manufacturing industry, modern production processes are increasingly challenging the machining standards for any workpiece being milled. Surface roughness is a key factor in determining its performance. Therefore, predicting the surface roughness of any workpiece is a pressing task. To enhance surface roughness prediction capabilities, researchers both domestically and internationally are dedicated to related research. In recent years, machine learning prediction has gained increasing popularity, primarily due to its robust predictive data capabilities. Artificial neural networks are the most widely used prediction method in machine learning.

[0003] However, when the BP neural network performs calculations, it has shortcomings such as poor convergence and easy to fall into local minimization. Although some people have used some algorithms to optimize the BP neural network to predict surface roughness, the calculation time is long, which reduces the calculation speed. Therefore, it is necessary to use a new algorithm to predict surface roughness to improve the prediction accuracy and calculation time. Summary of the Invention

[0004] Purpose of the invention:

[0005] This paper proposes an improved method for predicting the surface roughness of milled workpieces. Its primary purpose is to provide a method that can rapidly predict workpiece surface roughness under known conditions. This method utilizes a Northern Goshawk search algorithm improved with iterative chaotic mapping to globally optimize the initial weights and thresholds of the neural network structure, overcoming inherent limitations of the neural network, enhancing its predictive power and accuracy, and improving computational speed.

[0006] Technical solution:

[0007] A method for predicting the surface roughness of a milling workpiece, characterized by the following steps:

[0008] 1) Determine the topological structure of the BP neural network and store the experimental data obtained by milling workpieces with CNC machine tools in the form of a matrix. In the experimental data, the process parameters serve as the input data of the BP neural network, and the surface roughness value serves as the output data;

[0009] 2) Normalize the input data and output data through a normalization model;

[0010] 3) Determine the number of weights and thresholds required for optimization of the BP neural network according to the parameter number model, and map the weights and thresholds to the position of the northern goshawk, where the position of the northern goshawk is a vector;

[0011] 4) Setting the scale and number of iterations T of the northern goshawk, generating the initial population position of the northern goshawk through the initial position transformation model of the iterative chaotic mapping strategy, and forming the northern goshawk population position matrix X;

[0012] 5) Input the experimental data in step 1) into the BP neural network model, calculate the initial weight and the neural network prediction value under the threshold, and use the error function between the prediction value and the measured value as the fitness function F to calculate the fitness value of the northern goshawk position; arrange them in ascending order according to the fitness value, and the northern goshawk position with the minimum fitness value is the prey location P i ;

[0013] 6) Determine the current location of the prey P in step 5) i Afterwards, the northern goshawk approaches the prey, and in the process of approaching, the northern goshawk updates its position and re-determines the prey's position through the prey recognition model;

[0014] 7) After the prey position is re-determined, the fitness value of the prey position changes. The prey position is updated through the prey chasing and prey escape models. The updated fitness values ​​of the northern goshawk are arranged in ascending order. The northern goshawk with the smallest fitness value is the final prey position. When the number of iterations is terminated, the position of the northern goshawk at the final prey position is the optimized weight and threshold;

[0015] 8) Substitute the weights and thresholds optimized in step 7) into the BP neural network structure for training, and finally predict the surface roughness of the workpiece under different working conditions based on the training results.

[0016] Preferably, the initial position transformation model of the iterative chaotic mapping in step 4) is:

[0017]

[0018] In the formula, b is the control parameter, b is taken as 0.05, X i Represents the i-th initial individual of a randomly generated j-dimensional vector in [0,1].

[0019] Preferably, in step 4), the northern goshawk population position matrix X is:

[0020]

[0021] Where X is the population matrix of northern goshawk, X i is the position of the i-th northern goshawk, x i,j is the j-th dimension position of the i-th northern goshawk, N is the population size of the northern goshawk, and m is the dimension of the problem to be solved.

[0022] Preferably, the fitness function of the northern goshawk position in step 5) is expressed as:

[0023]

[0024] Where F is the objective function vector of the northern goshawk population, F i is the objective function value of the i-th northern goshawk. Preferably, the location P of the prey in step 5) i for:

[0025]

[0026] Where, P i is the prey location of the i-th northern goshawk; k1 is a random integer in the range [1, N]; N is the population size of the northern goshawk.

[0027] Preferably, the prey recognition model in step 6) is:

[0028]

[0029] Where, P i is the prey position of the i-th northern goshawk; is the fitness value of the prey position of the i-th northern goshawk; The new position of the i-th northern goshawk after the prey identification phase is updated; The new position of the jth dimension of the i-th northern goshawk after updating in the prey identification stage; is the fitness value of the i-th northern goshawk after the prey identification phase; r1' and r2' are random numbers in the range [0,1]; I is a random integer of 1 or 2;

[0030] Among them, the two nonlinear factor expressions are:

[0031] r1'=d·(1-(t / T) η ) 1 / η

[0032]

[0033] Where η is the adjustment coefficient, t is the current number of iterations, and T is the maximum number of iterations. In this paper, η = 1.5 and d = 0.05 are taken.

[0034] Preferably, the prey chasing and prey escape model in step 7) is:

[0035]

[0036] Where t is the current number of iterations and T is the maximum number of iterations; The new position of the i-th northern goshawk after updating for the prey pursuit and prey escape phases; The new position of the jth dimension of the i-th northern goshawk after updating for the prey chasing and prey escape stages; is the fitness value of the i-th northern goshawk after updating based on the prey chasing and prey escape stages.

[0037] Advantages and effects:

[0038] This method improves the Northern Goshawk algorithm and uses it to optimize the BP neural network. It effectively avoids the shortcomings of BP neural network predictions, such as susceptibility to local optima, poor convergence, and overfitting, and improves the time required to predict workpiece surface roughness under known conditions. The training prediction results obtained by the BP neural network, INGO-BP, and SSA-BP prediction methods were compared. Using average error rate and computation time as evaluation metrics for prediction performance, the improved NGO-BP training results showed a lower average error than both SSA-BP and traditional BP, resulting in higher prediction accuracy and shorter computation time. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 (a) is the fitness curve of the NGO algorithm; (b) is the fitness curve of the INGO algorithm;

[0040] Figure 2 This is the flow chart of the INGO-BP algorithm;

[0041] Figure 3 This is a comparison chart of training results;

[0042] Figure 4 Comparison chart of training results of test data. DETAILED DESCRIPTION

[0043] The present invention will be better described below with reference to the accompanying drawings.

[0044] The present invention is to predict the surface roughness of a workpiece after milling. Its significance lies in predicting the surface roughness values ​​corresponding to different process parameter combinations when milling the workpiece through surface quality prediction research, thereby providing a guarantee for selecting appropriate processing parameters and obtaining the ideal workpiece surface roughness value.

[0045] In order to improve the calculation time of predicting the surface roughness of workpieces under known conditions, an algorithm based on the improved Northern Goshawk search method to optimize BP neural network (INGO-BP) is proposed to address the shortcomings of BP neural network prediction, such as easy falling into local optimum, poor convergence, and easy overfitting. This algorithm optimizes the initial weights and thresholds of the BP neural network to improve the prediction accuracy and calculation time of the workpiece surface roughness after milling.

[0046] The foraging pattern of the northern goshawk in the northern goshawk algorithm (INGO):

[0047] 1) The northern goshawk is a medium-to-large raptor in the family Accipitridae and a carnivore. Its hunting strategy consists of two phases: the first is prey recognition, during which it attacks at high speeds. The second phase involves pursuit and prey escape, during which it pursues and captures its prey.

[0048] 2) During the prey identification stage, after determining the prey target, the northern goshawks move towards the prey and attack it.

[0049] 3) During the pursuit and prey escape phases, after attacking, the prey will attempt to escape. Therefore, the northern goshawk must continue to pursue the prey during the final stages of the pursuit. Because of their high pursuit speed, the northern goshawk can pursue and capture prey in almost any situation.

[0050] The principle of the BP neural network combined with the improved northern goshawk algorithm in the present invention is:

[0051] The number of input nodes, output nodes, and hidden layer nodes in the neural network are determined based on the input and output data, thereby determining the structure of the BP neural network. The input and output data are normalized using a normalization model and used as the input P and output T of the BP neural network structure, respectively. The initial weights and thresholds in the BP neural network are determined based on the parameter number model and mapped to the positions of northern goshawks. The northern goshawk population size and number of iterations are set, and an iterative chaotic mapping strategy is used to initialize the northern goshawk population position matrix X. The neural network predictions are then calculated based on the initial weights and thresholds. The error function between the predicted and measured values ​​is used as the fitness function F. Based on the northern goshawk's foraging rules in the northern goshawk search method, the fitness values ​​of the northern goshawk positions are calculated and sorted in ascending order. The northern goshawk position with the lowest fitness value is used as the prey position. The positions of the northern goshawks and their prey are continuously updated through attacking and chasing the prey. When the number of iterations reaches the end, the updated fitness values ​​of the northern goshawk positions are sorted in ascending order. The northern goshawk position with the minimum fitness value is the final prey position. The northern goshawk position at the prey position at this time is the optimized weight and threshold. The optimized weight and threshold of the BP neural network are substituted into the BP neural network for training. Based on the training results, the surface roughness values ​​of the workpiece under different working conditions are finally predicted.

[0052] like Figure 2 As shown, the present invention relates to a method for predicting the surface roughness of a workpiece milled by a CNC machine tool, which specifically comprises the following steps:

[0053] 1) Determine the topological structure of the BP neural network and store the experimental data obtained by milling workpieces with CNC machine tools in the form of a matrix. In the experimental data, the process parameters serve as the input data of the BP neural network, and the surface roughness value serves as the output data;

[0054] The number of training samples accounts for 85% of the total number of samples, and the number of test samples accounts for 15% of the total number of sample data.

[0055] The process parameters (taking the milling screw rotor as an example, the process parameters include spindle speed, intermittent feed rate, machining ratio, etc.) are used as the input data of the BP neural network, and the surface roughness value is used as the output data. The data is stored in a matrix form. According to the dimension m of the input matrix, the number of input layer neurons is determined to be m, and according to the dimension n of the output matrix, the number of output layer neurons is determined to be n. The number of hidden layer neurons is determined according to the hidden layer neuron model. The hidden layer neuron model is:

[0056]

[0057] Where k is the number of neurons in the hidden layer, m is the number of neurons in the input layer, n is the number of neurons in the output layer, and α is a constant with a value of [1,10].

[0058] 2) Normalize the input data and output data through a normalization model;

[0059] The normalized model is:

[0060]

[0061] Among them, y in the formula is the normalized data, X min is the minimum value of the sample data, X max is the maximum value of the sample data.

[0062] The input data and output data after sample normalization are used as the input data P and output data T of INGO-BP respectively.

[0063] 3) Determine the number of weights and thresholds required for optimization of the BP neural network according to the parameter number model, and map the weights and thresholds to the position of the northern goshawk, where the position of the northern goshawk is a vector;

[0064] The number of parameters in the network model is:

[0065] j=k(m+n+1)+n

[0066] Where j is the number of optimization parameters (weights and thresholds), k is the number of neurons in the hidden layer, m is the number of neurons in the input layer, and n is the number of neurons in the output layer. The parameters to be optimized are set to an upper limit of 1 and a lower limit of 0, limiting them to the range [0, 1].

[0067] 4) Set the scale of the northern goshawk and the number of iterations T (which can be set according to any experimental conditions), generate the initial population position of the northern goshawk through the initial position transformation model of the iterative chaotic mapping strategy, and form the northern goshawk population position matrix X;

[0068] The initial position transformation model of the northern goshawk population using iterative chaotic mapping is:

[0069]

[0070] In the formula, b is the control parameter, and b is taken as 0.05. i Represents the i-th initial individual of a randomly generated j-dimensional vector in [0,1].

[0071] The process of initializing the population is as follows;

[0072] First, a j-dimensional vector in the range [0, 1] is randomly generated as the initial individual. This initial individual is then substituted into Equation (1.1) and iterated for each dimension to generate i-1 new northern goshawk individuals. Finally, all northern goshawk individuals are mapped to the variable value range to generate the northern goshawk population position matrix. The initial population generated using iterative chaotic mapping is rich in diversity and evenly distributed in the solution space, preventing the algorithm from prematurely converging and falling into local optima, thereby improving the algorithm's optimization efficiency.

[0073] The location matrix X of the northern goshawk population is:

[0074]

[0075] Where X is the population matrix of northern goshawk, X i is the position of the i-th northern goshawk, x i,j is the j-th dimension position of the i-th northern goshawk, N is the population size of the northern goshawk, and m is the dimension of the problem to be solved.

[0076] 5) Input the experimental data in step 1) into the BP neural network model, calculate the initial weight and the neural network prediction value under the threshold, and use the error function between the prediction value and the measured value as the fitness function F to calculate the fitness value of the northern goshawk position; arrange them in ascending order according to the fitness value, and the northern goshawk position with the minimum fitness value is the prey location P i ;

[0077] The fitness function of the northern goshawk's position can be expressed as:

[0078]

[0079] Where F is the objective function vector of the northern goshawk population, F i is the objective function value of the i-th northern goshawk. The location of the prey P i The specific description is shown in formula (3):

[0080]

[0081] Where, P i is the prey location of the i-th northern goshawk; k1 is a random integer in the range [1, N]; N is the population size of the northern goshawk.

[0082] 6) Determine the current location of the prey P in step 5) i Afterwards, the northern goshawk approaches the prey, and in the process of approaching, the northern goshawk updates its position and re-determines the prey's position through the prey recognition model;

[0083] When the northern goshawk approaches its prey, a nonlinear factor is introduced to update the position of the northern goshawk. At the end of the prey recognition stage, when the fitness value of the i-th northern goshawk after the update in this stage is less than the fitness value of the prey position, the prey position is updated and the current i-th northern goshawk position is used as the new prey position. Conversely, if the fitness value of the i-th northern goshawk position after the update in this stage is greater than or equal to the fitness value of the prey position, the original prey position remains unchanged.

[0084] The prey recognition model is described as follows:

[0085]

[0086]

[0087] Where, P i is the prey position of the i-th northern goshawk; is the fitness value of the prey position of the i-th northern goshawk; The new position of the i-th northern goshawk after the prey identification phase is updated; The new position of the jth dimension of the i-th northern goshawk after updating in the prey identification stage; is the fitness value of the i-th northern goshawk after updating based on the prey identification stage; r is a random number in the range of [0,1]; I is a random integer of 1 or 2.

[0088] Among them, the two nonlinear factor expressions are:

[0089]

[0090] Where η is the adjustment coefficient, t is the current number of iterations, and T is the maximum number of iterations. In this paper, η = 1.5 and d = 0.05 are taken.

[0091] The addition of nonlinear factors r1′ and r2′ increases the global search capability of the NGO algorithm in this stage, thereby improving the global optimization effect of the Northern Goshawk algorithm in the prey identification stage.

[0092] 7) After the prey position is re-determined, the fitness value of the prey position changes. The prey position is updated through the prey chasing and prey escape models. The updated fitness values ​​of the northern goshawk are arranged in ascending order. The northern goshawk with the smallest fitness value is the final prey position. When the number of iterations is terminated, the position of the northern goshawk at the final prey position is the optimized weight and threshold.

[0093] After the prey recognition stage, the prey will flee after being attacked, and the northern goshawk will chase it. At this time, the prey position fitness value changes. With each update iteration, the northern goshawk's current position fitness value and the current prey position fitness value are re-judged. When the iteration requirements are met, the output northern goshawk position is the optimal weight and threshold of the BP neural network;

[0094] During the prey chasing and prey escaping stages, if the fitness value of the i-th northern goshawk position after the update is less than the current prey position fitness value, the prey position is updated and the current i-th northern goshawk position is used as the new prey position. Conversely, if the fitness value of the i-th northern goshawk position after the update is greater than or equal to the prey position fitness value, the current prey position remains unchanged. The iterative update continues.

[0095] The prey chasing and prey escape models are described as follows:

[0096]

[0097] Where t is the current iteration number and T is the maximum iteration number. The new position of the i-th northern goshawk after updating for the prey pursuit and prey escape phases; The new position of the jth dimension of the i-th northern goshawk after updating for the prey chasing and prey escape stages; is the fitness value of the i-th northern goshawk after updating based on the prey chasing and prey escape stages.

[0098] 8) Substitute the weights and thresholds optimized in step 7) into the BP neural network structure for training, and finally predict the surface roughness of the workpiece under different working conditions based on the training results.

[0099] In order to show that the improved Northern Goshawk algorithm (INGO) is superior to the original Northern Goshawk algorithm (NGO), the objective function F1 is used for verification. The expression of F1 is as follows (1.3):

[0100]

[0101] Set the maximum number of iterations to 100, and the calculation results are as follows Figure 2 As shown, Figure 1 (a) is the calculation result of the original Northern Goshawk algorithm (NGO). The NGO algorithm began to converge at the 18th iteration. Within the given parameter range, the minimum convergence value was 5.149e-15. Figure 1 (b) shows the results of the improved Northern Goshawk algorithm (INGO). The INGO algorithm converged at the fourth iteration, and within the given parameter range, the convergence minimum was 4.0852e-36. It can be seen that the improved Northern Goshawk algorithm converged in fewer iterations than the original Northern Goshawk algorithm, and the improved Northern Goshawk algorithm's minimum convergence value was also smaller than that of the original Northern Goshawk algorithm. Therefore, the improved Northern Goshawk algorithm converged faster and with higher accuracy.

[0102] Example 1

[0103] The experimental task of predicting the surface roughness of the screw rotor milling is carried out using a special screw milling machine as the processing equipment. In the process of milling the screw rotor, the factors affecting the surface roughness of the screw rotor include the machine tool spindle speed v, the intermittent feed rate f n , processing ratio Q, etc. The machine tool spindle speed v, intermittent feed rate f n , processing ratio Q as input, and the output is the surface roughness value.

[0104] (1) The experimental data of different working conditions are sorted as shown in Table 1:

[0105] Table 1 Experimental data

[0106]

[0107]

[0108] (2) The input P dimension is 3, so the number of input layer units is determined to be 3; the output T is one-dimensional, so the number of output layer units is determined to be 1. The number of hidden layer neurons is 5, the number of individuals in the initial population is i = 20, the maximum number of iterations is set to maxgen = 30, and the proportion of the training set is set to 85%.

[0109] (3) Based on the set parameters and experimental results, the BP neural network is optimized using the improved Northern Goshawk search algorithm, and the optimized network is trained. The training results are compared with the original BP neural network and the SSA-BP neural network, as shown in Figure 2. Figure 4 The specific values ​​of the prediction errors are shown in Table 2.

[0110] Table 2 Comparison of prediction results errors of three methods

[0111]

[0112]

[0113] according to Figure 3 As shown in Table 2, the BP neural network, SSA-BP neural network, and the proposed INGO-BP algorithm all predict surface roughness during screw rotor milling. Table 3 shows the initial experimental roughness data and the predicted roughness values ​​from the three prediction methods. The error values ​​are the differences between the three methods and the original data. The average prediction error of the improved BP neural network algorithm proposed in this paper is 3.2%, lower than the 3.751% of the SSA-BP and the 4.665% of the classic BP. Therefore, the proposed INGO-BP method achieves higher prediction accuracy and better performance.

[0114] (4) The last 8 groups of data from the experimental results are used as test data to verify the prediction accuracy of the model. The corresponding parameters are used as input and predictions are made according to the INGO-BP method, and compared with the original experimental data. Figure 4 The specific values ​​of the prediction errors are shown in Table 3.

[0115] Table 3 Comparison of prediction errors of test data using three methods

[0116]

[0117] according to Figure 4 As shown in Table 3, the lowest average error is 6.8% for the INGO-BP algorithm, followed by 10.625% for the SSA-BP algorithm, and finally 17.803% for the classic BP network. Under the same conditions, the computation time for the INGO-BP algorithm is 32 seconds, while that for the SSA-BP algorithm is 38 seconds. This indicates that the improved neural network algorithm employed in this paper can accurately and quickly predict surface roughness during the milling process of screw rotors.

[0118] In summary, this method can quickly predict the surface roughness of the workpiece under given conditions and improve the accuracy of the predicted surface roughness.

Claims

1. A method for predicting the surface roughness of a milling workpiece, characterized by: The steps are: 1) Determine the topological structure of the BP neural network and store the experimental data obtained by milling workpieces with CNC machine tools in the form of a matrix. In the experimental data, the process parameters serve as the input data of the BP neural network, and the surface roughness value serves as the output data; 2) Normalize the input data and output data through a normalization model; 3) Determine the number of weights and thresholds required for optimization of the BP neural network according to the parameter number model, and map the weights and thresholds to the position of the northern goshawk, where the position of the northern goshawk is a vector; 4) Setting the scale and number of iterations T of the northern goshawk, generating the initial population position of the northern goshawk through the initial position transformation model of the iterative chaotic mapping strategy, and forming the northern goshawk population position matrix X; 5) Input the experimental data in step 1) into the BP neural network model, calculate the initial weight and the neural network prediction value under the threshold, and use the error function between the prediction value and the measured value as the fitness function F to calculate the fitness value of the northern goshawk position; arrange them in ascending order according to the fitness value, and the northern goshawk position with the minimum fitness value is the prey location P i ; 6) Determine the current location P of the prey in step 5) i Afterwards, the northern goshawk approaches the prey, and in the process of approaching, it updates the position of the northern goshawk and re-determines the prey's position through the prey recognition model; 7) After the prey position is re-determined, the fitness value of the prey position changes. The prey position is updated through the prey chasing and prey escape models. The updated fitness values ​​of the northern goshawk are arranged in ascending order. The northern goshawk with the smallest fitness value is the final prey position. When the number of iterations is terminated, the position of the northern goshawk at the final prey position is the optimized weight and threshold; 8) Substitute the weights and thresholds optimized in step 7) into the BP neural network structure for training, and finally predict the surface roughness of the workpiece under different working conditions based on the training results.

2. The method for predicting the surface roughness of a milled workpiece according to claim 1, wherein: The initial position transformation model of the Iterative chaotic map in step 4) is: In the formula, b is the control parameter, b is taken as 0.05, X i Represents the i-th initial individual of a randomly generated j-dimensional vector in [0,1].

3. The method for predicting the surface roughness of a milled workpiece according to claim 1, wherein: In step 4), the position matrix X of the northern goshawk population is: Where X is the population matrix of northern goshawk, X i is the position of the i-th northern goshawk, x i,j is the j-th dimension position of the i-th northern goshawk, N is the population size of the northern goshawk, and m is the dimension of the problem to be solved.

4. The method for predicting the surface roughness of a milled workpiece according to claim 3, wherein: The fitness function of the northern goshawk position in step 5) is expressed as: Where F is the objective function vector of the northern goshawk population, F i is the objective function value of the i-th northern goshawk.

5. The method for predicting the surface roughness of a milled workpiece according to claim 4, wherein: The location P of the prey in step 5) i for: Where, P i is the prey location of the i-th northern goshawk; k1 is a random integer in the range [1, N]; N is the population size of the northern goshawk.

6. The method for predicting the surface roughness of a milled workpiece according to claim 3, wherein: Prey recognition model in step 6): Where, P i is the prey position of the i-th northern goshawk; is the fitness value of the prey position of the i-th northern goshawk; The new position of the i-th northern goshawk after the prey identification phase is updated; The new position of the jth dimension of the i-th northern goshawk after updating in the prey identification stage; is the fitness value of the i-th northern goshawk after the prey identification phase; r1' and r2' are random numbers in the range [0,1]; I is a random integer of 1 or 2; Among them, the two nonlinear factor expressions are: r1'=d·(1-(t / T) η ) 1 / η Where η is the adjustment coefficient, t is the current number of iterations, and T is the maximum number of iterations. In this paper, η = 1.5 and d = 0.05 are taken.

7. The method for predicting the surface roughness of a milled workpiece according to claim 3, wherein: The prey chasing and prey escape model in step 7) is: Where t is the current number of iterations and T is the maximum number of iterations; The new position of the i-th northern goshawk after updating for the prey pursuit and prey escape phases; The new position of the jth dimension of the i-th northern goshawk after updating for the prey chasing and prey escape stages; is the fitness value of the i-th northern goshawk after updating based on the prey chasing and prey escape stages.

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