TC4 high-speed milling process parameter multi-objective optimization method based on BPNN-tSSA algorithm

Abstract

The invention provides a TC4 high-speed milling process parameter multi-objective optimization method based on a BPNN-tSSA algorithm. The method comprises the steps that S1, the surface roughness, the energy consumption, the material removal rate and the subsurface damage serve as optimization targets, the cutting speed, the feeding speed, the axial cutting depth and the radial cutting depth serve as optimization variables, and an experiment scheme is constructed; s2, arranging a data set according to an experimental result, and dividing the data set into a training set # imgabs0 # and a test set # imgabs1 # according to a one-leaving cross validation method; respectively training the BPNN models to obtain a BPNN model set; s3, BPNN models of the surface roughness, the energy consumption, the material removal rate and the subsurface damage are constructed respectively, the root-mean-square error of a single BPNN model # imgabs2 # is calculated, and the overall fitting accuracy # imgabs5 # of a BPNN model set # imgabs4 # is verified through a test set # imgabs3 #; s4, constructing a multi-objective optimization model; s5, optimizing the process parameters by using an improved SSA algorithm to obtain corresponding milling parameters when the comprehensive evaluation index is optimal; according to the method, the parameters of the titanium alloy high-speed milling process can be optimized.

Description

Technical Field

[0001] The invention relates to the field of production and manufacturing technology, in particular to a multi-objective optimization method for TC4 high-speed milling process parameters based on a BPNN-tSSA algorithm. Background Art

[0002] Since the 1950s, due to the urgent needs of aerospace technology, the titanium industry has developed rapidly. Due to its excellent properties such as high specific strength, good heat resistance and corrosion resistance, titanium alloys have not only become an indispensable structural material in the modern aerospace industry, but also have been widely used in shipbuilding, chemical industry, metallurgy, medical treatment, etc. In the field of aerospace, titanium alloys are mainly used to manufacture compressor discs, turbine discs, blades and casings of jet engines, as well as structural parts such as large main landing gear support beams, rear fuselage sections and steering beams. Titanium alloys are also widely used in the navigation, energy, chemical industry and automotive industries, such as for the manufacture of propellers, pumps, valves and pipes and other parts that work in corrosive environments. In addition, titanium alloys have also been increasingly widely used in the automotive industry and in daily life fields such as medical equipment and sports equipment.

[0003] Titanium alloy has high specific strength and excellent corrosion resistance, and is an ideal aviation structural material. However, compared with structural steel, stainless steel and high-temperature alloy, titanium alloy is more sensitive to surface damage and defects, and is prone to fatigue fracture accidents. Therefore, it is of great practical significance to carry out research on improving cutting accuracy and quality to ensure that cutting products have good surface integrity.

[0004] At present, the cutting process of titanium alloys is mainly based on turning, milling and drilling, and the processing of aviation titanium alloy structural parts is mainly based on milling. When milling titanium alloys, due to the effect of cyclic thermal loads during the processing, the chips and the blade are easy to stick together, and the tool wear is serious. At this stage, most of the research focuses on optimization using traditional modeling methods, but for cutting processing, different machine tools and material differences will also lead to inaccuracy in traditional empirical formulas; a small number of them use machine learning algorithms for optimization, but most of them use native machine learning algorithms. Native machine learning algorithms have the disadvantages of being easy to mature prematurely and easy to fall into local optimality. Summary of the invention

[0005] The present invention proposes a multi-objective optimization method for TC4 high-speed milling process parameters based on a BPNN-tSSA algorithm, which belongs to a multi-objective optimization method for titanium alloy high-speed milling process parameters based on an improved BPNN-SSA algorithm. The method uses titanium alloy milling parameters (milling speed, feed speed, axial cutting depth, radial cutting depth) and titanium alloy surface roughness, energy consumption, material removal rate and sub-surface damage as data sets for a training model to form an optimization algorithm that combines BPNN with a sparrow search algorithm with a good point set and t-distribution adaptive variation, which can achieve the optimization of titanium alloy high-speed milling process parameters.

[0006] The present invention adopts the following technical solutions.

[0007] A multi-objective optimization method for TC4 high-speed milling process parameters based on BPNN-tSSA algorithm is used for optimizing titanium alloy high-speed milling process parameters, including the following steps;

[0008] Step S1: Taking the surface roughness, energy consumption, material removal rate and subsurface damage of milling titanium alloy material as optimization targets, and taking cutting speed, feed speed, axial cutting depth and radial cutting depth as optimization variables, an experimental plan is constructed;

[0009] Step S2: Arrange the data set according to the experimental results and divide the data set into training set D and training set D according to the leave-one-out cross-validation method. t and the test set D v ; Use k training sets D t1 ,D t2 …D tk Train the BPNN models separately and obtain the BPNN model set M = [M1, M2…M i …M k ];

[0010] Step S3: Construct BPNN models of surface roughness, energy consumption, material removal rate and subsurface damage respectively, and calculate the single BPNN model M i The root mean square error is obtained by testing the set D v Verify the overall fitting accuracy A of the BPNN model set M c ;

[0011] Step S4: Adopting the CRITIC method to perform objective weighting to establish a comprehensive evaluation function, and building a multi-objective optimization model in combination with the constraints of each process parameter;

[0012] Step S5: Use the improved SSA algorithm to optimize the process parameters and obtain the milling parameters corresponding to the optimal comprehensive evaluation index, thereby optimizing the titanium alloy milling process parameters.

[0013] Step S1 includes the following steps:

[0014] Step S1.1, select cutting speed V c , feed per tooth f z For experimental factors, set the levels of each factor and design orthogonal experiments;

[0015] Constraints of various factors set by titanium alloy high-speed milling conditions:

[0016] Cutting speed V min ≤V c ≤V max

[0017] Feed per tooth f min ≤f z ≤f max

[0018] in,

[0019] V min 、V max is the cutting speed V c The minimum and maximum values ​​of ;

[0020] f min 、f max is the feed speed f z The minimum and maximum values ​​of ;

[0021] Step S1.2, conduct milling experiments. After each milling experiment, measure the surface roughness, energy consumption, material removal rate, and sub-surface damage of the workpiece after milling, so as to organize the data set based on the experimental results.

[0022] Step S2 includes the following steps:

[0023] Step S2.1: After the experiment is completed, the data set is sorted according to the experimental results.

[0024] D={(x1,y1),(x2,y2),...(x i ,y i )...,(x k ,y k )}, according to the leave-one-out cross-validation method, the data set is divided into training set D t =[D t1 ,D t2 …D ti …D tk ] and the test set D v =[D v1 ,D v2 …D vi …D vk ].

[0025] Step S2.2: Convert the dimensionless expression into a dimensionless expression to ensure data comparability. Normalize the data set. The original independent variable is X = {x1, x2, ... x i ...,x k}, the normalization method is as follows

[0026] For positive indicators, the larger the value, the better: For the reverse indicator, the smaller the value, the better: The transformed data set is D = {(x g1 ,y1),(x g2 ,y2),...(x gi ,y i )...,(x gk ,y k )}.in,

[0027] x i is the initial value of the variable;

[0028] x gi is the normalized variable;

[0029] Max(x) is the maximum value of the original variable;

[0030] Min(x) is the minimum value of the original variable;

[0031] Step S2.3: Use training set D ti , train the BPNN model M i ;

[0032] Step S2.4: Randomly initialize the weight matrix between the input layer and the hidden layer

[0033] in,

[0034] d represents the number of neurons in the input layer;

[0035] q represents the number of neurons in the hidden layer;

[0036] Represents the connection weights between a single input layer and hidden layer neurons;

[0037] Step S2.5, randomly initialize the bias value of the input layer neurons connected to the hidden layer neurons;

[0038] Step S2.6: Randomly initialize the initial weight matrix of the hidden layer neurons connecting the output layer neurons

[0039] in,

[0040] l represents the number of neurons in the output layer;

[0041] Represents the connection weights between a single hidden layer and output layer neurons;

[0042] Step S2.7, randomly initialize the bias value of the hidden layer neurons connected to the output layer neurons;

[0043] Step S2.8, set the hidden layer activation function to

[0044] Step S2.9: Calculate the output of the neural network

[0045] Out o =f(w (ho) ·f(w (ih) ·x+b (ih) )+b (ho) )

[0046] in,

[0047]

[0048] Out ol Represents the output value of the lth output node;

[0049] Step S2.10: Calculate the loss function Loss of the neural network

[0050]

[0051] Among them, y i Represents the i-th label value;

[0052] Step S2.11, calculate the error factor δ0 between the output layer and the hidden layer

[0053]

[0054] Step S2.12: Update the weight w between the hidden layer and the output layer (ho) With bias b (ho)

[0055]

[0056] in,

[0057] Represents the updated weights between the hidden layer and the output layer;

[0058] Represents the updated bias between the hidden layer and the output layer;

[0059] η represents the learning rate, η>0.

[0060] Step S2.13, calculate the error factor δ between the input layer and the hidden layer i

[0061]

[0062] Step S2.14: Update the weight w between the hidden layer and the output layer (ih) With bias b (ih) ;

[0063]

[0064] in,

[0065] Represents the updated weights between the hidden layer and the output layer;

[0066] Represents the updated bias between the hidden layer and the output layer;

[0067] η represents the learning rate, η>0;

[0068] Step S2.15: Repeat steps S2.7 to S2.13 until the training error value Loss is less than the specified error threshold E, and finally obtain the BPNN model M. i ;

[0069] Step S2.16: According to the principle of leave-one-out cross-validation, repeat steps S2.1 to S2.14 k times until all k training sets have been trained for one round, and obtain the BPNN model set M = [M1, M2, ... M i ...M k ].

[0070] Step S3 includes the following steps:

[0071] Step S3.1, construct BPNN models of surface roughness, energy consumption, material removal rate and subsurface damage respectively, and calculate the root mean square error RMSE between the predicted value and the true value of a single BPNN model. The error calculation formula is:

[0072]

[0073] Step S3.2: Through the test set D v Verify the overall fitting accuracy A of the BPNN model set M c , the calculation formula of model fitting accuracy is:

[0074]

[0075] The step S4 comprises the following steps:

[0076] Step S4.1, use the forward or reverse method to process the data to retain the volatility differences between the indicators, so as to more effectively assign weights; the normalization formula is shown in step S2.2;

[0077] Step S4.2, calculate the variability index. In the CRITIC method, the standard deviation is used to measure the degree of fluctuation between data values. The larger the standard deviation of the index, the greater the difference between its data values, indicating that the index contains more information. Therefore, when evaluating, the index with a larger standard deviation should be regarded as more valuable and should be assigned a higher weight. The calculation is as follows;

[0078]

[0079] In the formula represents the mean of the jth target; f j represents the standard deviation of the j-th target;

[0080] Step S4.3, calculate the conflict index. The conflict index uses the correlation coefficient to quantify the correlation between the indicators. The stronger the correlation of the indicators, the smaller the conflict, and the more information content reflected together, thus showing more repetitiveness in the evaluation. In this case, the independent evaluation ability of the indicators is relatively weakened, so when allocating weights, such indicators should be given less weight. The calculation formula is as follows;

[0081]

[0082] In the formula, x i 、x j Represent targets i and j respectively; R ij is the correlation coefficient between targets i and j; Cov(x i ,x j ) represents the covariance of targets i and j; is the conflict index of target j;

[0083] Step S4.4, calculate the amount of information of each target, and the calculation formula is as follows;

[0084]

[0085] C j The larger it is, the more significant the role of the jth indicator in the evaluation index system is, and the higher the weight assigned to it should be;

[0086] Step S4.5, establish a comprehensive evaluation function, in which the smaller the surface roughness Sa, the energy consumption Power and the sub-surface damage Sd, the better; and the larger the material removal rate Cq, the better; in order to construct a multi-objective evaluation function, the attributes of the above four indicators need to be the same, so the material removal rate needs to be processed so that its attribute becomes as small as possible; the four indicators are pre-processed according to the normalization formula in step S2.2, f1(x) represents surface roughness, f2(x) represents energy consumption, f3(x) represents material removal rate, and f4(x) represents sub-surface damage. The specific formula is shown below;

[0087]

[0088] In the formula, x1 represents the surface roughness value; x2 represents the energy consumption value; x3 represents the material removal rate value; x4 represents the subsurface damage value, Sa min , Sa max Indicates the minimum and maximum values ​​of surface roughness, Power min ,Power max Indicates the minimum and maximum energy consumption, Cq min , Cq max Indicates the minimum and maximum values ​​of material removal rate, Sd min , Sd max Indicates the minimum and maximum values ​​of sub-surface damage; Step S4.6, after data preprocessing is completed, the weight coefficient is calculated through step S4.4, and the weight coefficient is assigned to each target to establish a comprehensive evaluation function, and its calculation formula is as follows;

[0089]

[0090] Step S4.7, transform the multi-objective optimization problem into a comprehensive index problem. The multi-objective optimization model is shown as follows:

[0091]

[0092] In the formula, F is the multi-objective optimization model, x tmin ≤x t ≤x tmax are the constraints on the optimization variables.

[0093] The step S5 comprises the following steps:

[0094] Step S5.1, using the improved SSA algorithm for optimization, obtaining the milling process parameters corresponding to the model when the optimal comprehensive index is obtained, thereby optimizing the milling process parameters;

[0095] Step S5.2, use the improved SSA algorithm to optimize the parameters; in the algorithm, there are N sparrow individuals, and the number of iterations is set to T, and the individual sparrow is initialized to X = {x 1 ,x 2 ,x 3 ,x 4}, let the first dimension be the cutting speed V c The second dimension is the feed per tooth f z Size, the third dimension is the axial cutting depth a p The fourth dimension is the radial depth of cut a e ; Set population variables for the four dimensions, and use the optimal point set generation method instead of the traditional random generation method to make the initial population more traversable, thereby better achieving the purpose of global optimization:

[0096] P i =[{d1*i},{d2*i},{d3*i},{d4*i}],i=1,2,...,N

[0097]

[0098]

[0099] in,

[0100] P i represents the set of good points corresponding to the sparrow numbered i;

[0101] {d j *i} represents the best point element corresponding to sparrow i in the jth dimension, and the value is d j *i decimal part;

[0102] p represents the smallest prime number that satisfies the constraint (p-2) / 2≥2;

[0103] Represents the value of the i-th sparrow in the j-th dimension;

[0104] represents the good point coefficient, corresponding to the element of the jth dimension in the good point set;

[0105] N represents the number of individuals in the sparrow population;

[0106] T represents the maximum number of iterations required;

[0107] m 1 ,u 1 Indicates the spindle speed V c Minimum and maximum values ​​on constraints;

[0108] m 2,u 2 Indicates the feed per tooth f z Minimum and maximum values ​​on constraints;

[0109] m 3 ,u 3 Indicates the axial cutting depth a p Minimum and maximum values ​​on constraints;

[0110] m 4 ,u 4 Indicates radial cutting depth a e Minimum and maximum values ​​on constraints;

[0111] Step S5.3: Substitute the initialized sparrow population individuals into the fitness function established in step S4.7 to obtain the sparrow's fitness value Y p ={y p1 ,y p2 ,...y pN};

[0112] in,

[0113] Y p represents the fitness value of the sparrow group;

[0114] y pi Represents the fitness value of individual sparrows;

[0115] Step S5.4, sort the fitness of the sparrow individuals, among which the sparrow individuals with better fitness are the discoverer sparrows PD, whose number generally accounts for 10% to 20% of the population. The discoverer PD is mainly responsible for searching for food in the environment and providing the location and direction for the entire sparrow group to find food; the remaining sparrow individuals are follower sparrows JD, which obtain food by following the discoverer PD; the two identities of the discoverer PD and the follower JD are not fixed, and the sparrow individuals can flexibly change their identities as the scene changes; another part of the sparrow individuals is set as the vigilant SD, indicating the individuals in the population who are aware of the danger, generally accounting for 10% to 20% of the total population, but this part is jointly borne by the discoverer and the joiner. Since the sparrow individuals SD close to the periphery are more vulnerable to attacks by outsiders during the predation process, the external sparrow individuals SD will constantly adjust their positions and move closer to the internal or adjacent companions to increase their own safety; Step S5.5, the sparrow population begins to forage, and the sparrow individuals move closer to the food. The formula for updating the discoverer position is as follows:

[0116]

[0117] in,

[0118] X ij Represents the position information of the i-th sparrow in the j-th dimension in the solution space;

[0119] t is the current iteration number of the algorithm, T is the exit of the algorithm, indicating the maximum number of iterations;

[0120] α is a random value in (0,1];

[0121] The value range of R is [0,1], which indicates the warning value of the individual sparrow chirping when encountering danger in the algorithm;

[0122] The value range of ST is [0.5, 1], which means that if the warning value of individual sparrows in the algorithm exceeds this threshold, they will move to a safe place to forage;

[0123] Q is a random number that satisfies the normal distribution;

[0124] L is a matrix of dimension l*d, where all elements are 1;

[0125] Step S5.6, when the discoverer PD searches for better food, the follower JD will leave his position to compete for the food of the discoverer PD. If he can grab the food, he will eat it to replenish his energy. If the follower JD does not get the food, he will be forced to search for food in other areas in order to obtain food energy. The follower JD position update formula is as follows:

[0126]

[0127] in,

[0128] X p It indicates the position with the most food among the discoverers, i.e. the position with the best fitness value;

[0129] X w Indicates the place with the worst fitness value in the current solution space;

[0130] A is a matrix of dimension l*d, where all elements are 1 or -1;

[0131] A * Satisfies the relationship A * =A T (AA T ) -1 ;

[0132] Step S5.7: When a sparrow encounters danger during the foraging process, it will move closer to the search circle or other companions. The position update formula of the alert SD is as follows:

[0133]

[0134] in,

[0135] X bIt is the position with the best fitness value in the global solution space of the current iteration;

[0136] β is a random value that satisfies the normal distribution with a mean of 0 and a variance of 1, which is called the step adjustment factor;

[0137] Z is a random value between [-1,1], indicating the direction in which the individual sparrow moves;

[0138] ε is a constant close to zero to prevent the denominator from being zero;

[0139] f i is the fitness value of the i-th sparrow individual in the current iteration;

[0140] f b It is the optimal value of fitness in the global solution space under the current iteration;

[0141] f w It is the worst fitness value in the global solution space under the current iteration;

[0142] When f i ≠f b When , it means that the i-th sparrow is on the periphery of the foraging circle and is more vulnerable to attacks from outsiders;

[0143] When f i =f b When , it means that some individual sparrows are aware of the danger and want to move closer to their companions to ensure their own safety;

[0144] Step S5.8, introduce dynamic selection probability p to adjust the use of adaptive t distribution mutation operator, and its calculation formula is as follows:

[0145] p=w1-w2×(T-iter) / T

[0146] in,

[0147] T is the maximum number of iterations;

[0148] iter is the current iteration number;

[0149] w1 determines the upper limit of the dynamic selection probability, and w2 determines the range of change of the dynamic selection probability;

[0150] Step S5.9, introduce the random number rand in [0,1], when rand>p, perform the adaptive t distribution mutation operation:

[0151]

[0152]

[0153] in,

[0154] is the new position of the i-th sparrow search individual in the population after mutation;

[0155] x i is the original position of the i-th sparrow individual in the population;

[0156] t(iter) satisfies the t distribution with the number of algorithm iterations iter as the degree of freedom;

[0157] Step S5.10: Repeat steps S5.2 to S5.3 to calculate the fitness Y of the sparrow population after mutation. p '={y' p1 ,y' p2 ,...y' pN}, compare Y′ p ,Y p The optimal fitness value in is, if Y′ p If it is better, replace the global optimal solution;

[0158] Step S5.11, perform iterative output. When the number of iterations is less than the maximum number of iterations T, perform iterative processing according to steps S5.3 to S5.10; when the generation condition is met, output the first sparrow position and its fitness value to obtain the optimal target solution of multi-objective optimization; among the position coordinates of the sparrow individual, the first dimension is the cutting speed V c The second dimension is the feed per tooth f z Size, the third dimension is the axial cutting depth a p The fourth dimension is the radial depth of cut a e .

[0159] In the milling process, the axial cutting depth and the radial cutting depth are determined by the machining process.

[0160] In the experiment, the axial cutting depth and the radial cutting depth were set to constant values.

[0161] The present invention is a multi-objective optimization method for titanium alloy high-speed milling process parameters based on an improved BPNN-SSA algorithm. The method uses titanium alloy milling parameters (milling speed, feed speed, axial cutting depth, radial cutting depth) and titanium alloy surface roughness, energy consumption, material removal rate and sub-surface damage as data sets for training models. It proposes an optimization algorithm that combines BPNN with a sparrow search algorithm with a good point set and t-distribution adaptive variation, which can achieve the optimization of titanium alloy high-speed milling process parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0162] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0163] Attached Figure 1It is a flow chart of the improved BPNN-SSA algorithm training of the present invention;

[0164] Attached Figure 2 This is a convergence diagram of the BPNN-SSA algorithm;

[0165] Attached Figure 3 It is a convergence diagram of the BPNN-tSSA algorithm of the present invention. DETAILED DESCRIPTION

[0166] As shown in the figure, the multi-objective optimization method of TC4 high-speed milling process parameters based on BPNN-tSSA algorithm is used for the optimization of titanium alloy high-speed milling process parameters, including the following steps;

[0167] Step S1: Taking the surface roughness, energy consumption, material removal rate and subsurface damage of milling titanium alloy material as optimization targets, and taking cutting speed, feed speed, axial cutting depth and radial cutting depth as optimization variables, an experimental plan is constructed;

[0168] Step S2: Arrange the data set according to the experimental results and divide the data set into training set D and training set D according to the leave-one-out cross-validation method. t and the test set D v ; Use k training sets D t1 ,D t2 …D tk Train the BPNN models separately and obtain the BPNN model set M = [M1, M2…M i …M k ];

[0169] Step S3: Construct BPNN models of surface roughness, energy consumption, material removal rate and subsurface damage respectively, and calculate the single BPNN model M i The root mean square error is obtained by testing the set D v Verify the overall fitting accuracy A of the BPNN model set M c ;

[0170] Step S4: Adopting the CRITIC method to perform objective weighting to establish a comprehensive evaluation function, and building a multi-objective optimization model in combination with the constraints of each process parameter;

[0171] Step S5: Use the improved SSA algorithm to optimize the process parameters and obtain the milling parameters corresponding to the optimal comprehensive evaluation index, thereby optimizing the titanium alloy milling process parameters.

[0172] Step S1 includes the following steps:

[0173] Step S1.1, select cutting speed V c , feed per tooth f zFor experimental factors, set the levels of each factor and design orthogonal experiments;

[0174] Constraints of various factors set by titanium alloy high-speed milling conditions:

[0175] Cutting speed V min ≤V c ≤V max

[0176] Feed per tooth f min ≤f z ≤f max

[0177] in,

[0178] V min 、V max is the cutting speed V c The minimum and maximum values ​​of ;

[0179] f min 、f max is the feed speed f z The minimum and maximum values ​​of ;

[0180] Step S1.2, conduct milling experiments. After each milling experiment, measure the surface roughness, energy consumption, material removal rate, and sub-surface damage of the workpiece after milling, so as to organize the data set based on the experimental results.

[0181] Step S2 includes the following steps:

[0182] Step S2.1: After the experiment is completed, the data set is sorted according to the experimental results.

[0183] D={(x1,y1),(x2,y2),...(x i ,y i )...,(x k ,y k )}, according to the leave-one-out cross-validation method, the data set is divided into training set D t =[D t1 ,D t2 …D ti …D tk ] and the test set D v =[D v1 ,D v2 …D vi …D vk ].

[0184] Step S2.2: Convert the dimensionless expression into a dimensionless expression to ensure data comparability. Normalize the data set. The original independent variable is X = {x1, x2, ... x i ...,x k}, the normalization method is as follows

[0185] For positive indicators, the larger the value, the better: For the reverse indicator, the smaller the value, the better: The transformed data set is D = {(x g1 ,y1),(x g2 ,y2),...(x gi ,y i )...,(x gk ,y k )}.

[0186] in,

[0187] x i is the initial value of the variable;

[0188] x gi is the normalized variable;

[0189] Max(x) is the maximum value of the original variable;

[0190] Min(x) is the minimum value of the original variable;

[0191] Step S2.3: Use training set D ti , train the BPNN model M i ;

[0192] Step S2.4: Randomly initialize the weight matrix between the input layer and the hidden layer

[0193]

[0194] in,

[0195] d represents the number of neurons in the input layer;

[0196] q represents the number of neurons in the hidden layer;

[0197] Represents the connection weights between a single input layer and hidden layer neurons;

[0198] Step S2.5, randomly initialize the bias value of the input layer neurons connected to the hidden layer neurons;

[0199] Step S2.6: Randomly initialize the initial weight matrix of the hidden layer neurons connecting the output layer neurons

[0200]

[0201] in,

[0202] l represents the number of neurons in the output layer;

[0203] Represents the connection weights between a single hidden layer and output layer neurons;

[0204] Step S2.7, randomly initialize the bias value of the hidden layer neurons connected to the output layer neurons;

[0205] Step S2.8, set the hidden layer activation function to

[0206] Step S2.9: Calculate the output of the neural network

[0207] Out o =f(w (ho) ·f(w (ih) ·x+b (ih) )+b (ho) )

[0208] in,

[0209]

[0210] Out ol Represents the output value of the lth output node;

[0211] Step S2.10: Calculate the loss function Loss of the neural network

[0212]

[0213] Among them, y i Represents the i-th label value;

[0214] Step S2.11, calculate the error factor δ0 between the output layer and the hidden layer

[0215]

[0216] Step S2.12: Update the weight w between the hidden layer and the output layer (ho) With bias b (ho)

[0217]

[0218] in,

[0219] Represents the updated weights between the hidden layer and the output layer;

[0220] Represents the updated bias between the hidden layer and the output layer;

[0221] η represents the learning rate, η>0.

[0222] Step S2.13, calculate the error factor δ between the input layer and the hidden layeri

[0223]

[0224] Step S2.14: Update the weight w between the hidden layer and the output layer (ih) With bias b (ih) ;

[0225]

[0226] in,

[0227] Represents the updated weights between the hidden layer and the output layer;

[0228] Represents the updated bias between the hidden layer and the output layer;

[0229] η represents the learning rate, η>0;

[0230] Step S2.15: Repeat steps S2.7 to S2.13 until the training error value Loss is less than the specified error threshold E, and finally obtain the BPNN model M. i ;

[0231] Step S2.16: According to the principle of leave-one-out cross-validation, repeat steps S2.1 to S2.14 k times until all k training sets have been trained for one round, and obtain the BPNN model set M = [M1, M2, ... M i ...M k ].

[0232] Step S3 includes the following steps:

[0233] Step S3.1, construct BPNN models of surface roughness, energy consumption, material removal rate and subsurface damage respectively, and calculate the root mean square error RMSE between the predicted value and the true value of a single BPNN model. The error calculation formula is:

[0234]

[0235] Step S3.2: Through the test set D v Verify the overall fitting accuracy A of the BPNN model set M c , the calculation formula of model fitting accuracy is:

[0236]

[0237] The step S4 comprises the following steps:

[0238] Step S4.1, use the forward or reverse method to process the data to retain the volatility differences between the indicators, so as to more effectively assign weights; the normalization formula is shown in step S2.2;

[0239] Step S4.2, calculate the variability index. In the CRITIC method, the standard deviation is used to measure the degree of fluctuation between data values. The larger the standard deviation of the index, the greater the difference between its data values, indicating that the index contains more information. Therefore, when evaluating, the index with a larger standard deviation should be regarded as more valuable and should be assigned a higher weight. The calculation is as follows;

[0240]

[0241] In the formula represents the mean of the jth target; f j represents the standard deviation of the j-th target;

[0242] Step S4.3, calculate the conflict index. The conflict index uses the correlation coefficient to quantify the correlation between the indicators. The stronger the correlation of the indicators, the smaller the conflict, and the more information content reflected together, thus showing more repetitiveness in the evaluation. In this case, the independent evaluation ability of the indicators is relatively weakened, so when allocating weights, such indicators should be given less weight. The calculation formula is as follows;

[0243]

[0244] In the formula, x i 、x j Represent targets i and j respectively; R ij is the correlation coefficient between targets i and j; Cov(x i ,x j ) represents the covariance of targets i and j; is the conflict index of target j;

[0245] Step S4.4, calculate the amount of information of each target, and the calculation formula is as follows;

[0246]

[0247] C j The larger it is, the more significant the role of the jth indicator in the evaluation index system is, and the higher the weight assigned to it should be;

[0248] Step S4.5, establish a comprehensive evaluation function, in which the smaller the surface roughness Sa, the energy consumption Power and the sub-surface damage Sd, the better; and the larger the material removal rate Cq, the better; in order to construct a multi-objective evaluation function, the attributes of the above four indicators need to be the same, so the material removal rate needs to be processed so that its attribute becomes as small as possible; the four indicators are pre-processed according to the normalization formula in step S2.2, f1(x) represents surface roughness, f2(x) represents energy consumption, f3(x) represents material removal rate, and f4(x) represents sub-surface damage. The specific formula is shown below;

[0249]

[0250] In the formula, x1 represents the surface roughness value; x2 represents the energy consumption value; x3 represents the material removal rate value; x4 represents the subsurface damage value, Sa min , Sa max Indicates the minimum and maximum values ​​of surface roughness, Power min ,Power max Indicates the minimum and maximum energy consumption, Cq min , Cq max Indicates the minimum and maximum values ​​of material removal rate, Sd min , Sd max Indicates the minimum and maximum values ​​of sub-surface damage; Step S4.6, after data preprocessing is completed, the weight coefficient is calculated through step S4.4, and the weight coefficient is assigned to each target to establish a comprehensive evaluation function, and its calculation formula is as follows;

[0251] F e (f1, f2, f3, f4) = W1 * f1(x)+W2 * f2(x)+W3 * f3(x)+W4 * f4(x)

[0252] Step S4.7, transform the multi-objective optimization problem into a comprehensive index problem. The multi-objective optimization model is shown as follows:

[0253]

[0254] In the formula, F is the multi-objective optimization model, x tmin ≤x t ≤x tmax are the constraints on the optimization variables.

[0255] The step S5 comprises the following steps:

[0256] Step S5.1, using the improved SSA algorithm for optimization, obtaining the milling process parameters corresponding to the model when the optimal comprehensive index is obtained, thereby optimizing the milling process parameters;

[0257] Step S5.2, use the improved SSA algorithm to optimize the parameters; in the algorithm, there are N sparrow individuals, and the number of iterations is set to T, and the individual sparrow is initialized to X = {x 1 ,x 2 ,x 3 ,x 4}, let the first dimension be the cutting speed V c The second dimension is the feed per tooth f z Size, the third dimension is the axial cutting depth a p The fourth dimension is the radial depth of cut a e ; Set population variables for the four dimensions, and use the optimal point set generation method instead of the traditional random generation method to make the initial population more traversable, thereby better achieving the purpose of global optimization:

[0258] P i =[{d1*i},{d2*i},{d3*i},{d4*i}],i=1,2,...,N

[0259]

[0260]

[0261] in,

[0262] P i represents the set of good points corresponding to the sparrow numbered i;

[0263] {d j *i} represents the best point element corresponding to sparrow i in the jth dimension, and the value is d j *i decimal part;

[0264] p represents the smallest prime number that satisfies the constraint (p-2) / 2≥2;

[0265] Represents the value of the i-th sparrow in the j-th dimension;

[0266] represents the good point coefficient, corresponding to the element of the jth dimension in the good point set;

[0267] N represents the number of individuals in the sparrow population;

[0268] T represents the maximum number of iterations required;

[0269] m 1 ,u1 Indicates the spindle speed V c Minimum and maximum values ​​on constraints;

[0270] m 2 ,u 2 Indicates the feed per tooth f z Minimum and maximum values ​​on constraints;

[0271] m 3 ,u 3 Indicates the axial cutting depth a p Minimum and maximum values ​​on constraints;

[0272] m 4 ,u 4 Indicates radial cutting depth a e Minimum and maximum values ​​on constraints;

[0273] Step S5.3: Substitute the initialized sparrow population individuals into the fitness function established in step S4.7 to obtain the sparrow's fitness value Y p ={y p1 ,y p2 ,...y pN};

[0274] in,

[0275] Y p represents the fitness value of the sparrow group;

[0276] y pi Represents the fitness value of individual sparrows;

[0277] Step S5.4, sort the fitness of the sparrow individuals, among which the sparrow individuals with better fitness are the discoverer sparrows PD, whose number generally accounts for 10% to 20% of the population. The discoverer PD is mainly responsible for searching for food in the environment and providing the location and direction for the entire sparrow group to find food; the remaining sparrow individuals are follower sparrows JD, which obtain food by following the discoverer PD; the two identities of the discoverer PD and the follower JD are not fixed, and the sparrow individuals can flexibly change their identities as the scene changes; another part of the sparrow individuals is set as the vigilant SD, indicating the individuals in the population who are aware of the danger, generally accounting for 10% to 20% of the total population, but this part is jointly borne by the discoverer and the joiner. Since the sparrow individuals SD close to the periphery are more vulnerable to attacks by outsiders during the predation process, the external sparrow individuals SD will constantly adjust their positions and move closer to the internal or adjacent companions to increase their own safety; Step S5.5, the sparrow population begins to forage, and the sparrow individuals move closer to the food. The formula for updating the discoverer position is as follows:

[0278]

[0279] in,

[0280] X ij Represents the position information of the i-th sparrow in the j-th dimension in the solution space;

[0281] t is the current iteration number of the algorithm, T is the exit of the algorithm, indicating the maximum number of iterations;

[0282] α is a random value in (0,1];

[0283] The value range of R is [0,1], which indicates the warning value of the individual sparrow chirping when encountering danger in the algorithm;

[0284] The value range of ST is [0.5, 1], which means that if the warning value of individual sparrows in the algorithm exceeds this threshold, they will move to a safe place to forage;

[0285] Q is a random number that satisfies the normal distribution;

[0286] L is a matrix of dimension l*d, where all elements are 1;

[0287] Step S5.6, when the discoverer PD searches for better food, the follower JD will leave his position to compete for the food of the discoverer PD. If he can grab the food, he will eat it to replenish his energy. If the follower JD does not get the food, he will be forced to search for food in other areas in order to obtain food energy. The follower JD position update formula is as follows:

[0288]

[0289] in,

[0290] X p It indicates the position with the most food among the discoverers, i.e. the position with the best fitness value;

[0291] X w Indicates the place with the worst fitness value in the current solution space;

[0292] A is a matrix of dimension l*d, where all elements are 1 or -1;

[0293] A * Satisfies the relationship A * =A T (AA T ) -1 ;

[0294] Step S5.7: When a sparrow encounters danger during the foraging process, it will move closer to the search circle or other companions. The position update formula of the alert SD is as follows:

[0295]

[0296] in,

[0297] X b It is the position with the best fitness value in the global solution space of the current iteration;

[0298] β is a random value that satisfies the normal distribution with a mean of 0 and a variance of 1, which is called the step adjustment factor;

[0299] Z is a random value between [-1,1], indicating the direction in which the individual sparrow moves;

[0300] ε is a constant close to zero to prevent the denominator from being zero;

[0301] f i is the fitness value of the i-th sparrow individual in the current iteration;

[0302] f b It is the optimal value of fitness in the global solution space under the current iteration;

[0303] f w It is the worst fitness value in the global solution space under the current iteration;

[0304] When f i ≠f b When , it means that the i-th sparrow is on the periphery of the foraging circle and is more vulnerable to attacks from outsiders;

[0305] When f i =f b When , it means that some individual sparrows are aware of the danger and want to move closer to their companions to ensure their own safety;

[0306] Step S5.8, introduce dynamic selection probability p to adjust the use of adaptive t distribution mutation operator, and its calculation formula is as follows:

[0307] p=w1-w2×(T-iter) / T

[0308] in,

[0309] T is the maximum number of iterations;

[0310] iter is the current iteration number;

[0311] w1 determines the upper limit of the dynamic selection probability, and w2 determines the range of change of the dynamic selection probability;

[0312] Step S5.9, introduce the random number rand in [0,1], when rand>p, perform the adaptive t distribution mutation operation:

[0313]

[0314] in,

[0315] is the new position of the i-th sparrow search individual in the population after mutation;

[0316] x i is the original position of the i-th sparrow individual in the population;

[0317] t(iter) satisfies the t distribution with the number of algorithm iterations iter as the degree of freedom;

[0318] Step S5.10: Repeat steps S5.2 to S5.3 to calculate the fitness Y′ of the sparrow population after mutation. p ={y' p1 ,y' p2 ,...y' pN}, compare Y′ p ,Y p The optimal fitness value in is, if Y′ p If it is better, replace the global optimal solution;

[0319] Step S5.11, perform iterative output. When the number of iterations is less than the maximum number of iterations T, perform iterative processing according to steps S5.3 to S5.10; when the generation condition is met, output the first sparrow position and its fitness value to obtain the optimal target solution of multi-objective optimization; among the position coordinates of the sparrow individual, the first dimension is the cutting speed V c The second dimension is the feed per tooth f z Size, the third dimension is the axial cutting depth a p The fourth dimension is the radial depth of cut a e .

[0320] In the milling process, the axial cutting depth and the radial cutting depth are determined by the machining process.

[0321] In the experiment, the axial cutting depth and the radial cutting depth were set to constant values.

[0322] Example:

[0323] In this example, a titanium alloy TC4 plate with a length of 100mm, a width of 100mm, and a thickness of 5mm is side milled on a VMC850E vertical machining center. Because in actual processing, the axial cutting depth and radial cutting depth are determined by the processing technology, so in this experiment, the axial cutting depth and radial cutting depth are set to fixed values, the axial cutting depth is taken as a fixed value of 0.2mm, the radial cutting depth is taken as a fixed value of 5mm, the cutting speed and the feed per tooth are taken at 4 levels, and a full factor experimental table is designed. The full factor experimental table is shown in Table 1.

[0324] Table 1 Factors and levels of full factorial experimental design

[0325]

[0326] Table 2 Full factorial experimental design table

[0327]

[0328] According to the experimental arrangement in Table 2, the titanium alloy TC4 plate with a length of 100mm, a width of 100mm, and a thickness of 5mm was profile milled. After the experiment, the surface roughness of the quality evaluation index after cutting needs to be measured, and the plane after the test is measured using a convenient handheld roughness measuring instrument. The measurement method is: after milling based on a set of process parameters, the surface roughness is measured three times and the average value is taken. Subsurface damage is measured by angle polishing method. The specific steps are to first grind and polish the workpiece from the side, then immerse the specimen in etching solution for etching, and finally place the workpiece sample under a scanning electron microscope, and observe the subsurface damage of the workpiece from the side in a direction perpendicular to the machined surface. Table 3 gives the data of the titanium alloy milling experiment.

[0329] Table 3 Titanium alloy milling experimental data

[0330]

[0331] (1) Constructing BPNN models for surface roughness, material removal rate, energy consumption, and subsurface damage

[0332] The present invention uses the CRITIC weight method to perform multi-objective fusion, so there are four BPNN models, corresponding to surface roughness, material removal rate, energy consumption and sub-surface damage respectively.

[0333] The model BPNNa with process parameters as output and TC4 high-speed milling surface roughness as output was constructed. Among them, the BPNN learning rate was set to η = 0.08, and the error threshold E = 0.01 was selected. The number of training cycles was set to 1000 times. There are 4 input layer nodes, namely cutting speed, feed per tooth, axial depth of cut and radial depth of cut (cutting depth is a constant), and 1 output layer node. It can be calculated from the empirical formula that the hidden layer nodes range from 2 to 9, and it is set to 7 after parameter adjustment experiments.

[0334] This example uses the leave-one-out cross-validation method. Table 4 lists the errors of the sixteen BPNN candidate models in the test set. The overall accuracy of the BPNN model after using the leave-one-out cross-validation method reaches 92.73%.

[0335] Table 4. Fitting error table of BPNNa candidate model

[0336]

[0337] It can be seen from Table 4 that the error of model 10 is the smallest, so model 10 is selected as the final surface roughness fitting model BPNNa.

[0338] The model BPNNb with process parameters as output and TC4 high-speed milling energy consumption as output was constructed. The BPNN learning rate was set to η = 0.05, and the error threshold E = 0.01 was selected. The number of training cycles was set to 800. The number of nodes in the input layer, output layer, and hidden layer was the same as that of the surface roughness BPNN model.

[0339] This example uses the leave-one-out cross-validation method. Table 5 lists the errors of the sixteen BPNN candidate models in the test set. The overall accuracy of the BPNN model after using the leave-one-out cross-validation method reaches 90.51%.

[0340] Table 5. BPNNb candidate model fitting error table

[0341]

[0342] It can be seen from Table 5 that the error of model 2 is the smallest, so model 2 is selected as the final energy consumption fitting model BPNNb.

[0343] The material removal rate model of TC4 high-speed milling can be obtained by mathematical modeling method, and the material removal rate model is represented by model c.

[0344] The model BPNNd with process parameters as output and TC4 high-speed milling subsurface damage as output was constructed. The BPNN learning rate was set to η = 0.07, and the error threshold E = 0.01 was selected. The number of training cycles was set to 500. The number of nodes in the input layer, output layer, and hidden layer was the same as that of the surface roughness BPNN model.

[0345] This example uses the leave-one-out cross-validation method. Table 6 lists the errors of the sixteen BPNN candidate models in the test set. The overall accuracy of the BPNN model after using the leave-one-out cross-validation method reaches 93.07%.

[0346] Table 6 BPNNd candidate model fitting error table

[0347]

[0348] It can be seen from Table 6 that model 15 has the smallest error, so model 15 is selected as the final sub-surface damage fitting model BPNNd.

[0349] (2) Constructing a multi-objective evaluation function

[0350] In this chapter, the CRITIC weight method is used for multi-objective fusion. The four objectives are weighted by calculation, and then the optimization algorithm is used to solve them. The CRITIC calculation weight coefficients are shown in Table 7.

[0351] Table 7 CRITIC weight coefficient table

[0352]

[0353] Substitute the weight coefficient of each objective into step S4.7 to construct a multi-objective comprehensive evaluation function, and the calculation formula is as follows.

[0354] F e (f1,f2,f3,f4)=0.452f1(x)+0.211f2(x)+0.151f3(x)+0.186f4(x)

[0355] On this basis, the upper and lower limits of the milling process parameters were set according to the critical conditions of the experimental equipment and experience, and a multi-objective optimization model was established with the goals of minimizing the surface roughness of TC4 high-speed milling, minimizing energy consumption, minimizing subsurface damage, and maximizing material removal rate. The calculation formula is as follows.

[0356]

[0357] In the formula, F e is a comprehensive evaluation function, x1 represents cutting speed, x2 represents feed per tooth, x3 represents axial cutting depth, and x4 represents radial cutting depth.

[0358] (3) Optimization of TC4 high-speed milling process parameters

[0359] The initial parameters of the SSA algorithm are set to population size N = 30, maximum number of iterations T = 100, the discoverers of the sparrow population account for 10% to 20% of the total, the follower sparrows account for 10% to 20%, and the rest are followers. Table 8 shows the process parameter values ​​obtained using the BPNN-SSA algorithm. Based on this process parameter, 7 TC4 high-speed milling experiments were repeated. The surface roughness, energy consumption, material removal rate and sub-surface damage obtained after taking the average value of the results are shown in Table 9. The algorithm convergence diagram is shown in Figure 2 Shown

[0360] Table 8 BPNN-SSA algorithm optimization process parameters

[0361]

[0362] Table 9 BPNN-SSA algorithm optimization process parameters milling experiment results

[0363]

[0364] The initial parameters of the tSSA algorithm are set to population size N = 30, maximum number of iterations T = 100, the discoverers of the sparrow population account for 10% to 20% of the total, the follower sparrows account for 10% to 20%, and the rest are followers. Table 10 shows the process parameter values ​​obtained using the BPNN-tSSA algorithm. Based on this process parameter, 7 TC4 high-speed milling experiments were repeated. The surface roughness, energy consumption, material removal rate and sub-surface damage obtained after taking the average value of the results are shown in Table 11. The algorithm convergence diagram is shown in Figure 3 shown.

[0365] Table 10 BPNN-tSSA algorithm optimization process parameters

[0366]

[0367] Table 11 BPNN-tSSA algorithm optimization process parameters milling experiment results

[0368]

[0369] As shown in the table above, the measured values ​​of the experiment using the process parameters optimized by the BPNN-tSSA algorithm are about 12% lower than the measured surface roughness values ​​of the experiment using the process parameters optimized by the BPNN-SSA algorithm in Table 9, the energy consumption is reduced by about 17%, the material removal rate is reduced by about 13%, and the sub-surface damage is increased by about 15%. After calculation, the comprehensive evaluation value of the BPNN-SSA algorithm is 0.328, and the comprehensive evaluation value of the BPNN-tSSA algorithm is 0.314. In comparison, the latter's comprehensive evaluation value is reduced by 4.25%. This shows that the BPNN-tSSA algorithm is more effective than the BPNN-SSA algorithm when performing multi-objective optimization of TC4 high-speed milling process parameters.

Claims

1. A multi-objective optimization method for TC4 high-speed milling process parameters based on BPNN-tSSA algorithm is used for the optimization of titanium alloy high-speed milling process parameters, which is characterized by: The steps include: Step S1: Taking the surface roughness, energy consumption, material removal rate and subsurface damage of milling titanium alloy material as optimization targets, and taking cutting speed, feed speed, axial cutting depth and radial cutting depth as optimization variables, an experimental plan is constructed; Step S2: Arrange the data set according to the experimental results and divide the data set into training set D and training set D according to the leave-one-out cross-validation method. t and the test set D v ; Use k training sets D t1 ,D t2 …D tk Train the BPNN models separately and obtain the BPNN model set M = [M1, M2…M i …M k ]; Step S3: Construct BPNN models of surface roughness, energy consumption, material removal rate and subsurface damage respectively, and calculate the single BPNN model M i The root mean square error is obtained by testing the set D v Verify the overall fitting accuracy A of the BPNN model set M c ; Step S4: Adopting the CRITIC method to perform objective weighting to establish a comprehensive evaluation function, and building a multi-objective optimization model in combination with the constraints of each process parameter; Step S5: Use the improved SSA algorithm to optimize the process parameters and obtain the milling parameters corresponding to the optimal comprehensive evaluation index, thereby optimizing the titanium alloy milling process parameters.

2. The multi-objective optimization method for TC4 high-speed milling process parameters based on BPNN-tSSA algorithm according to claim 1 is characterized in that: Step S1 includes the following steps: Step S1.1, select cutting speed V c , feed per tooth f z For experimental factors, set the levels of each factor and design orthogonal experiments; Constraints of various factors set by titanium alloy high-speed milling conditions: Cutting speed V min ≤V c ≤V max Feed per tooth f min ≤f z ≤f max in, V min 、V max is the cutting speed V c The minimum and maximum values ​​of ; f min 、f max is the feed speed f z The minimum and maximum values ​​of ; Step S1.2, conduct milling experiments. After each milling experiment, measure the surface roughness, energy consumption, material removal rate, and sub-surface damage of the workpiece after milling, so as to organize the data set based on the experimental results.

3. The multi-objective optimization method for TC4 high-speed milling process parameters based on BPNN-tSSA algorithm according to claim 2 is characterized in that: Step S2 includes the following steps: Step S2.1: After the experiment is completed, the data set is organized into D = {(x1, y1), (x2, y2), ... (x i ,y i )...,(x k ,y k )}, according to the leave-one-out cross-validation method, the data set is divided into training set D t =[D t1 ,D t2 …D ti …D tk ] and the test set D v =[D v1 ,D v2 …D vi …D vk ]. Step S2.2: Convert the dimensionless expression into a dimensionless expression to ensure data comparability. Normalize the data set. The original independent variable is X = {x1, x2, ... x i ...,x k }, the normalization method is as follows For positive indicators, the larger the value, the better: For inverse indicators where smaller values ​​are better: The transformed data set is D = {(x g1 ,y1),(x g2 ,y2),...(x gi ,y i )...,(x gk ,y k )}. in, x i is the initial value of the variable; x gi is the normalized variable; Max(x) is the maximum value of the original variable; Min(x) is the minimum value of the original variable; Step S2.3: Use training set D ti , train the BPNN model M i ; Step S2.4: Randomly initialize the weight matrix between the input layer and the hidden layer in, d represents the number of neurons in the input layer; q represents the number of neurons in the hidden layer; Represents the connection weights between a single input layer and hidden layer neurons; Step S2.5, randomly initialize the bias value of the input layer neurons connected to the hidden layer neurons; Step S2.6: Randomly initialize the initial weight matrix of the hidden layer neurons connecting the output layer neurons in, l represents the number of neurons in the output layer; Represents the connection weights between a single hidden layer and output layer neurons; Step S2.7, randomly initialize the bias value of the hidden layer neurons connected to the output layer neurons; Step S2.8, set the hidden layer activation function to Step S2.9: Calculate the output of the neural network Out o =f(w (ho) ·f(w (ih) ·x+b (ih) )+b (ho) ) in, Out ol Represents the output value of the lth output node; Step S2.10: Calculate the loss function Loss of the neural network Among them, y i Represents the i-th label value; Step S2.11, calculate the error factor δ0 between the output layer and the hidden layer Step S2.12: Update the weight w between the hidden layer and the output layer (ho) With bias b (ho) in, Represents the updated weights between the hidden layer and the output layer; Represents the updated bias between the hidden layer and the output layer; η represents the learning rate, η>0. Step S2.13, calculate the error factor δ between the input layer and the hidden layer i Step S2.14: Update the weight w between the hidden layer and the output layer (ih) With bias b (ih) ; in, Represents the updated weights between the hidden layer and the output layer; Represents the updated bias between the hidden layer and the output layer; η represents the learning rate, η>0; Step S2.15: Repeat steps S2.7 to S2.13 until the training error value Loss is less than the specified error threshold E, and finally obtain the BPNN model M. i ; Step S2.16: According to the principle of leave-one-out cross-validation, repeat steps S2.1 to S2.14 k times until all k training sets have been trained for one round, and obtain the BPNN model set M = [M1, M2, ... M i ...M k ].

4. The multi-objective optimization method for TC4 high-speed milling process parameters based on BPNN-tSSA algorithm according to claim 3 is characterized in that: Step S3 includes the following steps: Step S3.1, construct BPNN models of surface roughness, energy consumption, material removal rate and subsurface damage respectively, and calculate the root mean square error RMSE between the predicted value and the true value of a single BPNN model. The error calculation formula is: Step S3.2: Through the test set D v Verify the overall fitting accuracy A of the BPNN model set M c , the calculation formula of model fitting accuracy is:

5. The multi-objective optimization method for TC4 high-speed milling process parameters based on BPNN-tSSA algorithm according to claim 4 is characterized in that: The step S4 comprises the following steps: Step S4.1, use the forward or reverse method to process the data to retain the volatility differences between the indicators, so as to more effectively assign weights; the normalization formula is shown in step S2.2; Step S4.2, calculate the variability index. In the CRITIC method, the standard deviation is used to measure the degree of fluctuation between data values. The larger the standard deviation of the index, the greater the difference between its data values, indicating that the index contains more information. Therefore, when evaluating, the index with a larger standard deviation should be regarded as more valuable and should be assigned a higher weight. The calculation is as follows; In the formula represents the mean of the jth target; f j represents the standard deviation of the j-th target; Step S4.3, calculate the conflict index. The conflict index uses the correlation coefficient to quantify the correlation between the indicators. The stronger the correlation of the indicators, the smaller the conflict, and the more information content reflected together, thus showing more repetitiveness in the evaluation. In this case, the independent evaluation ability of the indicators is relatively weakened, so when allocating weights, such indicators should be given less weight. The calculation formula is as follows; In the formula, x i 、x j Represent targets i and j respectively; R ij is the correlation coefficient between targets i and j; Cov(x i ,x j ) represents the covariance of targets i and j; is the conflict index of target j; Step S4.4, calculate the amount of information of each target, and the calculation formula is as follows; C j The larger it is, the more significant the role of the jth indicator in the evaluation index system is, and the higher the weight assigned to it should be; Step S4.5, establish a comprehensive evaluation function, in which the smaller the surface roughness Sa, the energy consumption Power and the sub-surface damage Sd, the better; and the larger the material removal rate Cq, the better; in order to construct a multi-objective evaluation function, the attributes of the above four indicators need to be the same, so the material removal rate needs to be processed so that its attribute becomes as small as possible; the four indicators are pre-processed according to the normalization formula in step S2.2, f1(x) represents surface roughness, f2(x) represents energy consumption, f3(x) represents material removal rate, and f4(x) represents sub-surface damage. The specific formula is shown below; In the formula, x1 represents the surface roughness value; x2 represents the energy consumption value; x3 represents the material removal rate value; x4 represents the subsurface damage value, Sa min , Sa max Indicates the minimum and maximum values ​​of surface roughness, Power min ,Power max Indicates the minimum and maximum energy consumption, Cq min , Cq max Indicates the minimum and maximum values ​​of material removal rate, Sd min , Sd max Indicates the minimum and maximum values ​​of sub-surface damage; Step S4.6, after data preprocessing is completed, the weight coefficient is calculated through step S4.4, and the weight coefficient is assigned to each target to establish a comprehensive evaluation function, and its calculation formula is as follows; Step S4.7, transform the multi-objective optimization problem into a comprehensive index problem. The multi-objective optimization model is shown as follows: In the formula, F is the multi-objective optimization model, x tmin ≤x t ≤x tmax are the constraints on the optimization variables.

6. The multi-objective optimization method for TC4 high-speed milling process parameters based on BPNN-tSSA algorithm according to claim 5 is characterized in that: The step S5 comprises the following steps: Step S5.1, using the improved SSA algorithm for optimization, obtaining the milling process parameters corresponding to the model when the optimal comprehensive index is obtained, thereby optimizing the milling process parameters; Step S5.2, use the improved SSA algorithm to optimize the parameters; in the algorithm, there are N sparrow individuals, and the number of iterations is set to T, and the individual sparrow is initialized to X = {x 1 ,x 2 ,x 3 ,x 4 }, let the first dimension be the cutting speed V c The second dimension is the feed per tooth f z Size, the third dimension is the axial cutting depth a p The fourth dimension is the radial depth of cut a e ; Set population variables for the four dimensions, and use the optimal point set generation method instead of the traditional random generation method to make the initial population more traversable, thereby better achieving the purpose of global optimization: P i =[{d1*i},{d2*i},{d3*i},{d4*i}],i=1,2,...,N in, P i represents the set of good points corresponding to the sparrow numbered i; {d j *i} represents the best point element corresponding to sparrow i in the jth dimension, and the value is d j *i decimal part; p represents the smallest prime number that satisfies the constraint (p-2) / 2≥2; Represents the value of the i-th sparrow in the j-th dimension; represents the good point coefficient, corresponding to the element of the jth dimension in the good point set; N represents the number of individuals in the sparrow population; T represents the maximum number of iterations required; m 1 ,u 1 Indicates the spindle speed V c Minimum and maximum values ​​on constraints; m 2 ,u 2 Indicates the feed per tooth f z Minimum and maximum values ​​on constraints; m 3 ,u 3 Indicates the axial cutting depth a p Minimum and maximum values ​​on constraints; m 4 ,u 4 Indicates radial cutting depth a e Minimum and maximum values ​​on constraints; Step S5.3: Substitute the initialized sparrow population individuals into the fitness function established in step S4.7 to obtain the sparrow's fitness value Y p ={y p1 ,y p2 ,...y pN }; in, Y p represents the fitness value of the sparrow group; y pi Represents the fitness value of individual sparrows; Step S5.4, sort the fitness of the sparrow individuals, among which the sparrow individuals with better fitness are the discoverer sparrows PD, whose number generally accounts for 10% to 20% of the population. The discoverer PD is mainly responsible for searching for food in the environment and providing the location and direction for the entire sparrow group to find food; the remaining sparrow individuals are follower sparrows JD, which obtain food by following the discoverer PD; the two identities of the discoverer PD and the follower JD are not fixed, and the sparrow individuals can flexibly change their identities as the scene changes; another part of the sparrow individuals is set as the vigilant SD, indicating the individuals in the population who are aware of the danger, generally accounting for 10% to 20% of the total population, but this part is jointly borne by the discoverer and the joiner. Since the sparrow individuals SD close to the periphery are more vulnerable to attacks by outsiders during the predation process, the external sparrow individuals SD will constantly adjust their positions and move closer to the internal or adjacent companions to increase their own safety; Step S5.5, the sparrow population begins to forage, and the sparrow individuals move closer to the food. The formula for updating the discoverer position is as follows: in, X ij Represents the position information of the i-th sparrow in the j-th dimension in the solution space; t is the current iteration number of the algorithm, T is the exit of the algorithm, indicating the maximum number of iterations; α is a random value in (0,1]; The value range of R is [0,1], which indicates the warning value of the individual sparrow chirping when encountering danger in the algorithm; The value range of ST is [0.5, 1], which means that if the warning value of individual sparrows in the algorithm exceeds this threshold, they will move to a safe place to forage; Q is a random number that satisfies the normal distribution; L is a matrix of dimension l*d, where all elements are 1; Step S5.6, when the discoverer PD searches for better food, the follower JD will leave his position to compete for the food of the discoverer PD. If he can grab the food, he will eat it to replenish his energy. If the follower JD does not get the food, he will be forced to search for food in other areas in order to obtain food energy. The follower JD position update formula is as follows: in, X p It indicates the position with the most food among the discoverers, i.e. the position with the best fitness value; X w Indicates the place with the worst fitness value in the current solution space; A is a matrix of dimension l*d, where all elements are 1 or -1; A * Satisfies the relationship A * =A T (AA T ) -1 ; Step S5.7: When a sparrow encounters danger during the foraging process, it will move closer to the search circle or other companions. The position update formula of the alert SD is as follows: in, X b It is the position with the best fitness value in the global solution space of the current iteration; β is a random value that satisfies the normal distribution with a mean of 0 and a variance of 1, which is called the step adjustment factor; Z is a random value between [-1,1], indicating the direction in which the individual sparrow moves; ε is a constant close to zero to prevent the denominator from being zero; f i is the fitness value of the i-th sparrow individual in the current iteration; f b It is the optimal value of fitness in the global solution space under the current iteration; f w It is the worst fitness value in the global solution space under the current iteration; When f i ≠f b When , it means that the i-th sparrow is on the periphery of the foraging circle and is more vulnerable to attacks from outsiders; When f i =f b When , it means that some individual sparrows are aware of the danger and want to move closer to their companions to ensure their own safety; Step S5.8, introduce dynamic selection probability p to adjust the use of adaptive t distribution mutation operator, and its calculation formula is as follows: p=w1-w2×(T-iter) / T in, T is the maximum number of iterations; iter is the current iteration number; w1 determines the upper limit of the dynamic selection probability, and w2 determines the range of change of the dynamic selection probability; Step S5.9, introduce the random number rand in [0,1], when rand>p, perform the adaptive t distribution mutation operation: in, is the new position of the i-th sparrow search individual in the population after mutation; x i is the original position of the i-th sparrow individual in the population; t(iter) satisfies the t distribution with the number of algorithm iterations iter as the degree of freedom; Step S5.10: Repeat steps S5.2 to S5.3 to calculate the fitness Y of the sparrow population after mutation. p '={y' p1 ,y' p2 ,...y' pN }, compare Y' p ,Y p The optimal fitness value in is, if Y p If it is better, replace the global optimal solution; Step S5.11, perform iterative output. When the number of iterations is less than the maximum number of iterations T, perform iterative processing according to steps S5.3 to S5.10; when the generation condition is met, output the first sparrow position and its fitness value to obtain the optimal target solution of multi-objective optimization; among the position coordinates of the sparrow individual, the first dimension is the cutting speed V c The second dimension is the feed per tooth f z Size, the third dimension is the axial cutting depth a p The fourth dimension is the radial depth of cut a e .

7. The multi-objective optimization method for TC4 high-speed milling process parameters based on BPNN-tSSA algorithm according to claim 1 is characterized in that: In the milling process, the axial cutting depth and the radial cutting depth are determined by the machining process.

8. The multi-objective optimization method for TC4 high-speed milling process parameters based on BPNN-tSSA algorithm according to claim 1 is characterized in that: In the experiment, the axial cutting depth and the radial cutting depth were set to constant values.

Images