Multi-objective optimization method for turning process parameters of silicon-aluminum alloy based on improved BPNN-DE algorithm

Abstract

The application provides a silicon-aluminum alloy turning process parameter multi-objective optimization method based on an improved BPNN-DE algorithm, first, a BPNN model taking a cutting speed, a feed speed and a cutting depth as input and taking a surface roughness, a material removal rate and energy consumption as output is built, and the DE algorithm is improved to improve population diversity and optimization ability of the original DE algorithm, then the output of the BPNN model is combined with a geometric mean method to serve as fitness value of the improved DE algorithm, finally, the improved BPNN-DE algorithm is used to optimize the turning process parameters, and the improved BPNN-DE algorithm has good optimization effect compared with the unimproved BPNN-DE algorithm.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of production and manufacturing, and particularly relates to a turning process parameter multi-objective optimization method for a silicon-aluminum alloy based on an improved BPNN-DE algorithm. BACKGROUND

[0002] Due to the high strength, good wear resistance and low cost of silicon-aluminum alloy, the silicon-aluminum alloy is widely used in aerospace and automobile parts manufacturing, such as automobile pistons, cylinder sleeves and brake discs. However, due to the presence of silicon particles in the silicon-aluminum alloy, the tool for machining the silicon-aluminum alloy will be greatly worn, resulting in reduced workpiece surface roughness and production efficiency.

[0003] Ensuring the workpiece surface roughness while minimizing the efficiency and energy consumption has become a major concern in today's manufacturing industry. In the production process, cutting parameters are important factors that affect the workpiece cutting efficiency, total energy consumption and surface roughness. Therefore, to improve the turning roughness, production efficiency and reduce energy consumption in the production process of silicon-aluminum alloy, it is of great significance to explore the turning process parameter multi-objective optimization with the surface roughness, material removal rate and energy consumption of silicon-aluminum alloy as the target for the manufacturing, promotion and practical application of silicon-aluminum alloy products.

[0004] At present, in the process parameter optimization method of silicon-aluminum alloy turning, most methods still take a single target (surface roughness) as the optimization target, and few methods ensure the optimal material removal rate and energy consumption while optimizing the surface roughness.

[0005] The methods for optimizing the turning process parameters of silicon-aluminum alloy mainly include the following three kinds: first, using finite element analysis software to simulate the turning process and then optimizing the parameters. This method needs to consider the complex underlying mechanism in the turning process of the workpiece, and the mechanical properties of the material are different in different processing conditions and environments, so the parameter optimization using this method is not accurate. Second, the experimental method, which summarizes the change rule between the optimization target and the turning process parameters through a large number of turning experiments, and then gives suggestions manually or uses methods such as range analysis and variance analysis to optimize the process parameters. The disadvantage of this method is that it is difficult to learn the influence of parameter changes on the optimization target in the turning process. The third is the method based on swarm intelligence optimization, which automatically learns the spatial distribution of experimental data by establishing a mathematical model of the data, and combines intelligent optimization algorithm to find the optimal solution in the spatial distribution. This method not only avoids the complex underlying mechanism in turning, but also can find the optimal result in the solution space after learning the distribution of the data, and has the advantages of simple implementation, good optimization effect, etc.

[0006] At present, the proportion of methods based on swarm intelligence optimization algorithm for turning process parameter optimization of silicon aluminum alloy is gradually increasing, but the following shortcomings exist in the current methods:

[0007] First, most of the turning process parameter optimization methods of silicon aluminum alloy only consider a single optimization target, such as surface roughness, material removal rate, etc. Few methods consider optimizing the workpiece surface roughness while ensuring the efficiency and energy consumption to be optimal.

[0008] Second, the method for establishing the fitness function of most multi-objective optimization problems of turning process parameters of silicon aluminum alloy is ideal point method, weighted method or multiplication and division method. These comprehensive index methods can represent the good and bad of the comprehensive index to a certain extent, but they are not comprehensive enough and cannot overcome the situation where a certain index is poor but the comprehensive index is still excellent.

[0009] Third, in the method of turning process parameter optimization of silicon aluminum alloy, the objective function of most swarm intelligence optimization methods is a regression model with weak fitting of the nonlinear relationship between cutting parameters and optimization targets. However, in real processing, there is a universal nonlinear relationship between cutting parameters and optimization targets. Therefore, the existing methods have poor data fitting effect, and the existing swarm intelligence optimization methods are mostly not improved, with the disadvantages of poor population diversity and weak optimization ability. SUMMARY

[0010] In view of the shortcomings of the above prior art solutions, the purpose of the present application is to provide a multi-objective optimization method for turning process parameters of silicon aluminum alloy based on improved BPNN-DE algorithm. The method provides an improved BPNN-DE algorithm combining back propagation neural network (BPNN) and improved differential evolution algorithm (DE) for turning data fitting and multi-objective optimization. The geometric mean method is used to consider the workpiece surface roughness, material removal rate and energy consumption in multi-objective optimization. The optimized turning process parameters can ensure that the comprehensive index of surface roughness, material removal rate and energy consumption is optimal.

[0011] The method first builds a BPNN model with cutting speed, feed speed and cutting depth as input and surface roughness, material removal rate and energy consumption as output. The DE algorithm is improved to improve the population diversity and optimization ability of the original DE algorithm. Then the output of the BPNN model is combined with the geometric mean method as the fitness value of the improved DE algorithm. Finally, the improved BPNN-DE algorithm is used to optimize the turning process parameters, and the optimization effect of the improved BPNN-DE algorithm is better than that of the unimproved BPNN-DE algorithm.

[0012] The application solves its technical problems by adopting the technical scheme of:

[0013] A silicon-aluminum alloy turning process parameter multi-objective optimization method based on an improved BPNN-DE algorithm, characterized by comprising the following steps:

[0014] Step S1: Turning three elements: cutting speed, cutting depth, and feed rate are taken as factors to perform a turning full-factor experiment on a silicon-aluminum alloy bar, measure the surface roughness, material removal rate, and energy consumption of each group of experiments, and use them as a data set R for step S2 to establish a BPNN model;

[0015] Step S2: Turning three elements are taken as input features, and the measured surface roughness after turning, calculated material removal rate, and collected energy consumption are taken as outputs to build a silicon-aluminum alloy turning process parameter multi-objective optimization BPNN model.

[0016] Step S3: The DE algorithm is used to optimize the surface roughness, material removal rate, and energy consumption three targets separately to find the optimal value and the worst value of each target, then combine the BPNN model output value trained in step S2 to establish a fitness function by using the geometric mean method to comprehensively optimize the target, and finally use the improved DE algorithm to obtain the cutting parameters corresponding to the optimal fitness value.

[0017] Further, step S1 specifically comprises the following steps:

[0018] Step S11: Divide the data set R into K, K>1 parts, the maximum is The mutually exclusive subsets R K , R K =[R1,R2…R K ], len(R) represents the number of data in the data set R, represents the upward rounding symbol.

[0019] Step S12: Take the union set of K-1 mutually exclusive subsets R K as the training set C t , and the remaining subset as the test set C v , repeat the above process K times to obtain K training sets, C t =[C t1 ,C t2 …C tK ], and K test sets, C v =[C v1 ,C v2 …C vK ].

[0020] Further, step S2 specifically comprises the following steps:

[0021] Step S21: Combine K training sets C t1 C t2 …C tK Train BPNN models separately to obtain K BPNN models M1, M2...M K ;

[0022] Step S22: From K training sets C t1 C t2 …C tK Select any training set and train the BPNN model M1.

[0023] Step S23: Let the selected training set data be x = [x1, x2, ... x2]. t ], y = [y1, y2…y t ], t represents the number of training set data, y t Indicates the corresponding x t The tag value;

[0024] Step S24: Randomly initialize the initial weight matrix w connecting the input layer neurons to the hidden layer neurons. (ih) :

[0025]

[0026] in,

[0027] n represents the number of neurons in the input layer;

[0028] m represents the number of neurons in the hidden layer;

[0029] This represents the connection weight between the nth input layer neuron and the mth hidden layer neuron;

[0030] Step S25: Randomly initialize the bias values ​​b for the connections between the input layer neurons and the hidden layer neurons. (ih) ;

[0031] Step S26: Randomly initialize the initial weight matrix w connecting the hidden layer neurons to the output layer neurons. (ho) :

[0032]

[0033] in,

[0034] l represents the number of neurons in the output layer;

[0035] This represents the connection weight between the m-th hidden layer neuron and the l-th output layer neuron;

[0036] Step S27: Randomly initialize the bias value b of the hidden layer neuron connection output layer neuron (ho) ;

[0037] Step S28: Set the hidden layer activation function as

[0038] Step S29: Calculate the hidden layer output:

[0039] Out h = f(w (ih) · x + b (ih) )

[0040] wherein,

[0041]

[0042] Out hm denotes the output value of the mth hidden layer neuron;

[0043] Step S210: Calculate the output layer output:

[0044] Out o = f(w (ho) · Out h + b (ho) )

[0045] wherein,

[0046]

[0047] Out ol denotes the output value of the lth output layer neuron;

[0048] Step S211: Calculate the loss function:

[0049]

[0050] wherein, y i denotes the ith label value;

[0051] Step S212: Calculate the error factor δ0 between the output layer and the hidden layer:

[0052]

[0053] Step S213: Update the weight w (ho) and the bias b (ho) between the hidden layer and the output layer:

[0054]

[0055] wherein,

[0056] This represents the updated weights between the hidden layer and the output layer;

[0057] This indicates the offset between the updated hidden layer and the output layer;

[0058] η represents the learning rate, where η > 0;

[0059] Step S214: Calculate the error factor δ between the input layer and the hidden layer. i :

[0060]

[0061] Step S215: Update the weights w between the input layer and the hidden layer. (ih) With bias b (ih) :

[0062]

[0063] in,

[0064] This represents the updated weights between the input layer and the hidden layer;

[0065] This indicates the bias between the updated input layer and the hidden layer;

[0066] η represents the learning rate, where η > 0;

[0067] Step S216: Repeat steps S26 to S212 n times, n>0 times, until the training error Loss value is less than the specified error threshold E, and finally obtain the BPNN model M1;

[0068] Step S217: Repeat steps S21 to S213 K, K>1 times until all K training sets have been trained once, resulting in the BPNN model set M = [M1, M2, ..., M]. K ];

[0069] Step S218: Using test set C v =[C v1 C v2 …C vK The test BPNN model set M = [M1, M2, ..., M] K The fitting accuracy A c =[A c1 A c2 …A cK ]

[0070] The formula for calculating the model fitting accuracy is:

[0071]

[0072] Step S219: take the model with the highest model fitting rate as the multi-objective optimization model M A .

[0073] Further, step S3 specifically comprises the following steps:

[0074] Step S31: initialize the improved differential evolution model parameters as follows:

[0075] N p = s

[0076] Ch = r

[0077]

[0078] XOVR = q

[0079] MAXGEN = k

[0080] F = t

[0081] Encoding = RI

[0082] wherein,

[0083] N p = s indicates that the population size is s, s > 0;

[0084] Ch = r indicates that the number of gene positions of each individual in the population is r, r > 0;

[0085] indicates that the mutation probability is

[0086] XOVR = q indicates that the recombination probability is q, 0 < q < 1;

[0087] MAXGEN = k indicates that the maximum evolution generation number is k, k > 0;

[0088] F = t indicates that the differential scaling factor is t, 0 < t < 1;

[0089] Encoding = RI indicates that the encoding mode adopts real integer RI;

[0090] Step S32: define the parent population:

[0091] z = [z1, z2…z p …z s ]

[0092] wherein,

[0093] z indicates the parent population;

[0094] z prepresents the pth, 1≤p≤s individual in the parent population;

[0095] z s represents the last s th individual in the parent population;

[0096] Step S33: Introduce the Gaussian chaos mapping method to instantiate the parent population:

[0097]

[0098] wherein,

[0099] represents

[0100] represents the pth, 1≤p≤s individual in the parent population after Gaussian chaos mapping;

[0101] represents the last s th individual in the parent population after Gaussian chaos mapping;

[0102] z + represents the parent population after Gaussian chaos mapping;

[0103] Step S34: According to the elite copy selection strategy, the elite individuals are selected from the parent population and directly transmitted into the child population, and the rest of the individuals are subjected to selection, crossover and mutation operations. The specific method is as follows:

[0104] Step S341: Calculate the parent fitness value:

[0105]

[0106]

[0107] wherein,

[0108] M represents the BPNN model with the highest fitting accuracy;

[0109] represents the parent individual fitness value set;

[0110] represents the descending order of the individual fitness values from the best to the worst, the best;

[0111] Step S342: Select the corresponding individual is directly transmitted into the child population z c ;

[0112] Step S35: Introduce the Gaussian mutation process:

[0113]

[0114] wherein,

[0115] rand represents a random number obeying uniform distribution between (0, 1);

[0116] N(0, 1) represents a standard Gaussian distribution with mean 0 and variance 1;

[0117] represents the pth individual in the population after Gaussian mutation, 1≤p≤s;

[0118] represents the population after Gaussian mutation;

[0119] F represents a difference scaling factor;

[0120] represents the pth individual in the population after difference, 1≤p≤s; represents the pth individual in the population after difference, 1≤p≤s;

[0121] represents the pth individual in the population after difference, 1≤p≤s;

[0122] represents the population after difference;

[0123] Step S36: binomial distribution crossover is performed on the population after Gaussian mutation and the parent population:

[0124]

[0125]

[0126] wherein,

[0127] represents the pth individual in the population after crossover, 1≤p≤s;

[0128] represents the population after crossover;

[0129] Step S37: one-to-one survival selection strategy is implemented to obtain a new generation of offspring population z c

[0130]

[0131] z c = [z c1 ,z c2 …z cp …z cs ]

[0132] wherein,​

[0133] represents the fitness value of the pth (1≤p≤s) individual of the population after crossover;

[0134] represents the fitness value of the pth (1≤p≤s) individual of the parent population after Gaussian chaos;

[0135] z c represents the offspring population;

[0136] z cp represents the pth (1≤p≤s) individual of the offspring population;

[0137] z cs represents the last s th individual of the offspring population;

[0138] Step S38: repeating steps S34 to S37 with the offspring population z c as the parent population until the set number of generations n, and taking the individual with the optimal fitness value among all individuals of n generations as the optimal process parameter individual;

[0139] Step S39: assuming that there are K (K=b+v) objectives in total, b minimum objectives and v maximum objectives, separately optimizing the K objectives by steps S31 to S38 to obtain the minimum value β and the maximum value γ of each objective for use in the following step of calculating the fitness function of the multi-objective optimization model;

[0140] Step S310: calculating the performance index η A of the output value of the multi-objective optimization model M h ; j ;

[0141] For the minimum objectives, the performance index is represented as:

[0142]

[0143] wherein,

[0144] β h is the minimum value of the h th minimum objective;

[0145] γ h is the maximum value of the h th minimum objective;

[0146] M Ah (X) represents the model M A outputting the value of the h th minimum objective in the output value;

[0147] η h =[η1,η2,…,η b] represents a set of indexes of b minimization problems;

[0148] For the maximization problem, the performance index is expressed as:

[0149]

[0150] wherein,

[0151] β j is the minimum value of the jth maximization objective;

[0152] γ j is the maximum value of the jth maximization objective;

[0153] M Aj (X) represents a model M A value of the jth maximization objective in the output value;

[0154] η j =[η1,η2,…,η v ] represents a set of indexes of v maximization problems;

[0155] Step S311: taking the geometric mean of all target performance indexes as the total index η

[0156]

[0157] When η is larger and tends to 1, it indicates that the input model M A is better, and when η is smaller and tends to 0, the individual is worse;

[0158] Step S312: repeating steps S31 to S38, replacing the parent fitness value formula calculated in step S341 with in step S311, and taking the individual with the η value closest to 1 in n generations as the optimal process parameter individual.

[0159] Compared with the prior art, the present application and the preferred schemes thereof have the following advantages:

[0160] (1) The BPNN with high-precision fitting for nonlinear relationships is used to fit the turning data, and an improved strategy based on Gaussian chaos and mutation is introduced from the population generation and mutation strategy to improve the optimization ability of the DE algorithm, so that the optimization method has good optimization effect.

[0161] (2) The geometric mean method is used to comprehensively consider three objectives, avoiding the situation that when a certain index is poor and other indexes are good, the comprehensive index indicates that the cutting parameter is acceptable, but in fact the poor index will lead to unqualified machining workpieces. BRIEF DESCRIPTION OF DRAWINGS

[0162] The application will be described in further detail below with reference to the drawings and specific embodiments.

[0163] Figure 1 is a flow chart of the improved BPNN-DE algorithm training of the embodiments of the application. DETAILED DESCRIPTION

[0164] In order to make the features and advantages of the patent more obvious and easy to understand, the following specific examples are described in detail as follows:

[0165] It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present application. Unless otherwise indicated, all technical and scientific terms used in the specification have the same meaning as commonly understood by one of ordinary skill in the art to which the present application belongs.

[0166] It should be noted that the terms used herein are only for the purpose of describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, the singular form is intended to include the plural form unless the context clearly indicates otherwise, and it should also be understood that when the terms "comprise" and / or "include" are used in the specification, there is a feature, step, operation, device, component and / or combination thereof.

[0167] As shown in Figure 1 , the method for multi-objective optimization of turning process parameters of silicon-aluminum alloy based on the improved BPNN-DE algorithm provided by the embodiments includes the following steps:

[0168] (1) Taking the three cutting elements (cutting speed, cutting depth, and feed rate) as factors, a full-factor experiment is performed on the turning of silicon-aluminum alloy bars, the surface roughness, material removal rate, and energy consumption corresponding to each group of experiments are measured, and they are used as a data set R for the establishment of a BPNN model in step (2):

[0169] (1.1) The data set R is divided into K (K>1) mutually exclusive subsets R with a maximum size of K , denoted as R K =[R1,R2…R K ], len(R) represents the number of data in the data set R, and represents the upward rounding symbol.

[0170] (1.2) The union of K-1 mutually exclusive subsets R K is taken as the training set C t , and the remaining subset is taken as the test set C v . The above process is repeated K times to obtain K training sets, denoted as C t =[C t1 ,C t2 …CtK ], get K test sets, record C v = [C v1 , C v2 …C vK ].

[0171] (2) Take the three elements of turning as input features, and the surface roughness, material removal rate and energy consumption measured after turning as output, build a BPNN model for multi-objective optimization of turning process parameters of silicon-aluminum alloy. The specific steps are as follows:

[0172] (2.1) Train BPNN model respectively from K training sets C t1 , C t2 …C tK , get K BPNN models M1, M2…M K .

[0173] (2.2) Select one training set from K training sets C t1 , C t2 …C tK arbitrarily, such as C t1 , train BPNN model M1.

[0174] (2.3) Set the data in training set C t1 as x = [x1, x2…x t ], y = [y1, y2…y t ], t represents the number of training set data, y t represents the label value corresponding to x t .

[0175] (2.4) Randomly initialize the initial weight matrix w (ih)

[0176]

[0177] Wherein,

[0178] n represents the number of input layer neurons;

[0179] m represents the number of hidden layer neurons;

[0180] represents the connection weight between the nth input layer neuron and the mth hidden layer neuron

[0181] (2.5) Randomly initialize the bias value b (ih)

[0182] (2.6) Randomly initialize the initial weight matrix w (ho)

[0183]

[0184] where,

[0185] l denotes the number of output layer neurons;

[0186] denotes the connection weight between the mth hidden layer neuron and the lth output layer neuron.

[0187] (2.7) Randomly initialize the bias value b of the hidden layer neuron connecting the output layer neuron (ho)

[0188] (2.8) Set the hidden layer activation function as

[0189] (2.9) Calculate the hidden layer output

[0190] Out h = f(w (ih) · x + b (ih) )

[0191] where,

[0192]

[0193] Out hm denotes the output value of the mth hidden layer neuron.

[0194] (2.10) Calculate the output layer output

[0195] Out o = f(w (ho) · Out h + b (ho) ) where,

[0196]

[0197] Out ol denotes the output value of the lth output layer neuron.

[0198] (2.11) Calculate the loss function

[0199]

[0200] where, y i denotes the ith label value.

[0201] (2.12) Calculate the error factor δ0 between the output layer and the hidden layer

[0202]

[0203] (2.13) Update the weights w between the hidden layer and the output layer (ho) and the bias b (ho)

[0204]

[0205] wherein,

[0206] denotes the updated weights w between the hidden layer and the output layer;

[0207] denotes the updated bias b between the hidden layer and the output layer;

[0208] η denotes the learning rate, η > 0.

[0209] (2.14) Calculate the error factor δ between the input layer and the hidden layer i

[0210]

[0211] (2.15) Update the weights w between the input layer and the hidden layer (ih) and the bias b (ih)

[0212]

[0213] wherein,

[0214] denotes the updated weights w between the input layer and the hidden layer;

[0215] denotes the updated bias b between the input layer and the hidden layer;

[0216] η denotes the learning rate, η > 0.

[0217] (2.16) Repeat the processes of (2.6) to (2.12) n (n > 0) times until the training error Loss value is less than the specified error threshold E, and finally obtain the BPNN model M1

[0218] (2.17) Repeat the processes of (2.1) to (2.13) K (K > 1) times until all K training sets are trained for one round, and obtain the BPNN model set M = [M1, M2…M K ]

[0219] (2.18) Test the fitting accuracy A of the BPNN model set M = [M1, M2…M K ] with the test set C v = [C v1 , C v2 …C vK ]c = [A c1 ,A c2 …A cK ]

[0220] The calculation formula of model fitting accuracy is:

[0221]

[0222] (2.19) Take the model with the highest model fitting rate as the multi-objective optimization model M A

[0223] (3) Use DE algorithm to optimize surface roughness, material removal rate and energy consumption three targets separately, find out the optimal value and the worst value of each target, then combine the output value of the BPNN model trained in step (2), use geometric mean method to establish fitness function, finally use DE algorithm to get the corresponding cutting parameters when the fitness value is optimal. The specific method is as follows:

[0224] (3.1) Initialize the improved differential evolution model parameters as follows:

[0225] N p =s

[0226] Ch=r

[0227]

[0228] XOVR=q

[0229] MAXGEN=k

[0230] F=t

[0231] Encoding=RI

[0232] Among them,

[0233] N p =s represents the population size s (s>0);

[0234] Ch=r represents that the number of genes of each individual in the population is r (r>0);

[0235] represents that the mutation probability is

[0236] XOVR=q represents that the recombination probability is q (0

[0237] MAXGEN=k represents that the maximum evolution generation is k (k>0);

[0238] F=t represents that the differential scaling factor is t (0

[0239] Encoding=RI means that the encoding method adopts RI (real integer).

[0240] (3.2) Defining the parent population

[0241] z = [z1, z2…z p …z s ]

[0242] wherein,

[0243] z represents the parent population;

[0244] z p represents the pth (1≤p≤s) individual in the parent population;

[0245] z s represents the last s th individual in the parent population.

[0246] (3.3) Introducing the Gaussian chaos mapping method to instantiate the parent population

[0247]

[0248] wherein,

[0249] represents

[0250] represents the pth (1≤p≤s) individual in the parent population after the Gaussian chaos mapping;

[0251] represents the last s th individual in the parent population after the Gaussian chaos mapping;

[0252] z + represents the parent population after the Gaussian chaos mapping.

[0253] (3.4) According to the elite copy selection strategy, the elite individuals are selected from the parent population and directly transmitted into the child population, and the rest of the individuals are subjected to selection, crossover and mutation operations. The specific method is as follows:

[0254] (3.4.1) Calculating the parent fitness value

[0255]

[0256] wherein,

[0257] M represents the BPNN model with the highest fitting accuracy;

[0258] represents the parent individual fitness value set;

[0259] denotes the individual fitness values ordered in descending order from the best to the worst, best.

[0260] (3.4.2) Selection corresponding individual directly transmitting the offspring population z c

[0261] (3.5) Introducing Gaussian mutation process

[0262]

[0263]

[0264] where,

[0265] rand denotes a random number obeying uniform distribution in (0, 1);

[0266] N(0, 1) denotes a standard Gaussian distribution with mean 0 and variance 1;

[0267] denotes the p-th (1≤p≤s) individual in the population after Gaussian mutation;

[0268] denotes the population after Gaussian mutation;

[0269] F denotes the difference scaling factor;

[0270] denotes the p-th (1≤p≤s) individual in the population after difference; denotes the p-th (1≤p≤s) individual in the population after difference;

[0271] denotes the population after difference. (3.6) Binomial distribution crossover combining the Gaussian mutation population and the parent population

[0272]

[0273] where,

[0274]

[0275] denotes the p-th (1≤p≤s) individual in the population after crossover;

[0276] denotes the population after crossover;

[0277] ​​(3.7) Implement one-to-one survival selection strategy to get new sub-population z c

[0278]

[0279] z c = [z c1 , z c2 …z cp …z cs ]

[0280] wherein,

[0281] represents the fitness value of the pth (1≤p≤s) individual of the population after crossover;

[0282] represents the fitness value of the pth (1≤p≤s) individual of the parent population after Gaussian chaos.

[0283] z c represents the offspring population;

[0284] z cp represents the pth (1≤p≤s) individual of the offspring population;

[0285] z cs represents the last s individual of the offspring population.

[0286] (3.8) Repeat steps (3.4) to (3.7) with the offspring population z c as the parent population until the set number of generations n (n>0) times, and the individual with the optimal fitness value among all individuals of n generations is taken as the optimal process parameter individual.

[0287] (3.9) Assuming that there are K (K=b+v) objectives in total, b minimum objectives and v maximum objectives, the K objectives are respectively optimized by steps (3.1) to (3.8) to obtain the minimum value β and the maximum value γ of each objective, which are used for the fitness function calculation of the multi-objective optimization model in the following steps.

[0288] wherein,

[0289] (3.10) For the multi-objective optimization model M A , the performance index η h , η j is respectively calculated.

[0290] For the minimum objective, the performance index is represented as:

[0291]

[0292] wherein,

[0293] β h is the minimum value of the hth minimization objective;

[0294] γ h is the maximum value of the hth maximization objective;

[0295] M Ah (X) represents the model M A the value of the hth minimization objective in the output value;

[0296] η h = [η1, η2, …, η b ] represents the index set of the b minimization problems.

[0297] For the maximization problem, the performance index is represented as:

[0298]

[0299] where,

[0300] β j is the minimum value of the jth maximization objective;

[0301] γ j is the maximum value of the jth maximization objective;

[0302] M Aj (X) represents the model M A the value of the jth maximization objective in the output value;

[0303] η j = [η1, η2, …, η v ] represents the index set of the v maximization problems.

[0304] (3.11) takes the geometric mean of all target performance indices as the total index η

[0305]

[0306] When η is larger and tends to 1, it means that the input model M A is better, and when η is smaller and tends to 0, the individual is worse.

[0307] (3.12) repeats steps (3.1) to (3.8), replaces the formula for calculating the parent fitness value in step (3.4.1) with in (3.11), and takes the individual with the η value closest to 1 in the n generations as the optimal process parameter individual.

[0308] The above design is combined with an actual case to more fully demonstrate the embodiment scheme:

[0309] The case is carried out on the numerical control lathe CAK3665, and the diameter D of the silicon aluminum alloy bar is 60 mm, and the length H is 250 mm. The cutting speed, feed rate and cutting depth are taken as the experimental cutting parameters. In this experiment, the cutting speed and feed rate are taken as four levels. Considering the actual machining, the cutting depth is often given, so the cutting depth is taken as a fixed value. The specific levels of cutting speed and feed rate are shown in Table 1, and the levels of each factor are represented by numbers from 1 to 4. The full-factor experimental design table designed according to Table 1 is shown in Table 2, and the numbers 1 to 16 represent each test, the factors are represented by A to B, and the levels are represented by 1 to 4. The factors and levels in Table 2 correspond to Table 1.

[0310] Table 1 Full-factor experimental design factor and level table

[0311]

[0312] Table 2 Full-factor experimental design table

[0313]

[0314]

[0315] According to Table 2, the outer circle turning of the silicon aluminum alloy bar with diameter D of 60 mm and length H of 250 mm is carried out. In this experiment, the surface roughness, material removal rate and energy consumption of the cutting quality evaluation index need to be measured. Table 3 shows the measured surface roughness, material removal rate and energy consumption of the silicon aluminum alloy bar with diameter D of 60 mm and length H of 250 mm after turning. The measurement method is as follows: based on a group of process parameters, the surface roughness is measured four times after turning and the average value is taken, the material removal rate is determined by the ratio of material removal amount to time, and the energy consumption is obtained by the workshop bottom layer Internet of Things system. Since the cutting depth is determined by the machining allowance, considering the tool tip radius and the actual machining condition, the cutting depth is taken as a fixed value of 0.3 mm, and Table 3 shows the data of the silicon aluminum alloy turning experiment.

[0316] Table 3 Silicon aluminum alloy turning experiment data

[0317]

[0318]

[0319] (1) BPNN model parameter setting

[0320] The super parameters and neural network structure of the BPNN model need to be specified before the training of the BPNN model. The learning rate η represents the rate of updating the weights and biases in each iteration process of the neural network. If η is too small, the updating of the weights and biases will be slow, and the convergence speed of the model will be slow. If η is too large, the model will always be difficult to converge. After comprehensive consideration, the BPNN model selects η = 0.05. The training error threshold E of the neural network represents the termination condition of the neural network training iteration. If the error threshold E is too small, the model is prone to overfitting. If the error threshold E is too large, the model is prone to underfitting. After comprehensive consideration, the BPNN model selects E = 0.1. The neural network with a three-layer structure has the ability to fit any complex function. Therefore, the BPNN model in this case selects a three-layer neural network model. The number of input layer neurons is 3, which corresponds to the cutting speed, feed rate, and cutting depth. The number of hidden layer neurons is 6 after repeated experiments, which is more appropriate. The number of output layer neurons is 3, which is the surface roughness, material removal rate, and energy consumption of the machined surface quality evaluation index. The data obtained by the full-factor experiment is used to train the BPNN model, and a machine learning model that can map the nonlinear relationship between the turning process parameters and the turning surface quality, material removal rate, and energy consumption is obtained.

[0321] (2) Improved DE algorithm parameter setting

[0322] In this case, the results obtained by training the BPNN model are combined with the geometric mean method as the fitness function of the improved DE algorithm to optimize the turning process parameters of silicon-aluminum alloy. The initial parameter settings of the improved DE algorithm are as follows: RI (real integer) coding is used for coding, N p = 100 represents the population size of 100; Ch = 3 represents the number of gene bits of each individual in the population; = 0.1 represents the mutation probability; XOVR = 0.8 represents the recombination probability of 0.8; MAXGEN = 500 represents the maximum evolution generation of 500; F = 0.4 represents the difference scaling factor of 0.4;

[0323] (3) Multi-objective optimization model M A (z) and its constraints

[0324]

[0325] wherein,

[0326] M A (z) represents the BPNN model, and the output is the surface roughness, material removal rate, and energy consumption.

[0327]

[0328] wherein,

[0329] represents the 1st, 2nd, 3rd gene of the pth (1≤p≤s) individual in the population.

[0330] (4) BPNN fitting results

[0331] Table 4 lists the accuracy of the BPNN model in the test set. Since 5-fold cross-validation is used, there are 5 candidate models, numbered 1 to 5.

[0332] Table 4 BPNN model test set accuracy table

[0333] BPNN model number 1 2 3 4 5 Model results 91.86％ 96.33％ 94.81％ 93.68％ 86.18％

[0334] Select the best model 2 in Table 4 for subsequent step calculation.

[0335] (5) Unimproved DE algorithm optimization results

[0336] The process parameter values (cutting speed, cutting depth, feed rate) obtained by using the unimproved BPNN-DE algorithm are shown in Table 5, based on which the turning parts are processed, the surface roughness of the parts is measured four times and the average value is taken, and the material removal rate and energy consumption are shown in Table 6

[0337] Table 5 Unimproved BPNN-DE algorithm optimization process parameter table

[0338]

[0339] Table 6 Unimproved BPNN-DE algorithm optimization test result table

[0340]

[0341] The total index value of the measured results optimized by the unimproved BPNN-DE algorithm is calculated by the total index formula in the specific embodiment (3.11) as

[0342] (6) Improved DE algorithm optimization results

[0343] The process parameter values (cutting speed, cutting depth, feed rate) obtained by using the improved BPNN-DE algorithm are shown in Table 7, based on which the turning parts are processed, the surface roughness of the parts is measured four times and the average value is taken, and the material removal rate and energy consumption are shown in Table 8

[0344] Table 7 Improved BPNN-DE algorithm optimization process parameter table

[0345]

[0346] Table 8 Improved BPNN-DE algorithm optimization test result table

[0347]

[0348] The total index value of the measured results optimized by the improved BPNN-DE algorithm is calculated from the total index formula in the specific embodiment (3.11) and is

[0349] As can be seen from the comparison between Table 6 and Table 8, the surface roughness and material removal rate in the measured results optimized by the improved BPNN-DE algorithm are better than those in the measured results optimized by the unimproved BPNN-DE algorithm, the comprehensive index of the measured results optimized by the improved BPNN-DE algorithm is improved by 7.3% than that of the measured results optimized by the unimproved BPNN-DE algorithm, which indicates that the improved BPNN-DE algorithm can effectively perform multi-objective optimization on the turning process parameters of the silicon-aluminum alloy.

[0350] The above only describes the preferred embodiments of the present application, and any changes and modifications made within the scope of the present application should be included in the scope of the present application.

[0351] The above only describes the preferred embodiments of the present application, and is not intended to limit the present application in other forms, and any person skilled in the art can modify or change the above disclosed technical content into equivalent embodiments. However, any simple modification, equivalent change and modification made according to the technical essence of the present application to the above embodiments still belongs to the protection scope of the technical solution of the present application.

[0352] The present application is not limited to the above preferred embodiments, and anyone can derive other various forms of multi-objective optimization methods for turning process parameters of silicon-aluminum alloy based on the improved BPNN-DE algorithm under the inspiration of the present application, and any changes and modifications made within the scope of the present application should be included in the scope of the present application.

Claims

1. A multi-objective optimization method for silicon-aluminum alloy turning process parameters based on an improved BPNN-DE algorithm, characterized in that, Includes the following steps: Step S1: Using the three turning elements—cutting speed, depth of cut, and feed rate—as factors, conduct a full-factor turning experiment on silicon-aluminum alloy bars, measure the surface roughness, material removal rate, and energy consumption corresponding to each group of experiments, and use it as dataset R for step S2 to build a BPNN model. Step S2: Using the three turning elements as input features, and the measured surface roughness, calculated material removal rate, and collected energy consumption after turning as outputs, a multi-objective optimization BPNN model for silicon-aluminum alloy turning process parameters is constructed. The BPNN model is a three-layer neural network with 3 neurons in the input layer, corresponding to cutting speed, feed rate, and depth of cut, 6 neurons in the hidden layer, and 3 neurons in the output layer, corresponding to the surface quality evaluation indicators after cutting: surface roughness, material removal rate, and energy consumption. Step S3: Optimize the three objectives of surface roughness, material removal rate, and energy consumption separately using the DE algorithm to find the optimal and worst values ​​of each objective. Then, combine the output values ​​of the BPNN model trained in step S2 and use the geometric mean method to integrate the objectives to establish a fitness function. The geometric mean method is as follows: For the minimization objective, the performance metric is expressed as: in, β h Let be the minimum value of the h-th minimization objective; γ h Let be the maximum value of the h-th minimized objective; M Ah (X) represents model M A The value of the h-th minimized objective in the output values; η h =[η1,η2,…,η b ] represents the set of indices for b minimization problems; For the maximization problem, the performance metric is expressed as: in, β j Let be the minimum value of the j-th maximized objective; γ j Let be the maximum value of the j-th maximization objective; M Aj (X) represents model M A The j-th maximized value in the output; η j =[η1,η2,…,η v [] represents the set of indices for v maximization problems; The geometric mean of all target performance indicators is used as the total indicator η. Finally, the improved DE algorithm is used to obtain the cutting parameters corresponding to the model when the fitness value is optimal; the improvement of the DE algorithm includes introducing a Gaussian chaotic mapping method to instantiate the parent population, introducing a Gaussian mutation process, and combining the Gaussian mutated population with the parent population to perform binomial distribution crossover.

2. The multi-objective optimization method for silicon-aluminum alloy turning process parameters based on the improved BPNN-DE algorithm according to claim 1, characterized in that: Step S1 specifically includes the following steps: Step S11: Divide the dataset R into K parts, where K > 1, with a maximum size of [missing value]. Mutually exclusive subset R K , note R K = [R1,R2…R K ], where len(R) represents the number of data entries in dataset R. Indicates the rounding up symbol; Step S12: Select K-1 mutually exclusive subsets R K The union of the sets is used as the training set C. t The remaining subset is used as the test set. This process is repeated K times to obtain K training sets, denoted as C. t =[C t1 C t2 …C tK We obtain K test sets, denoted as C. v =[C v1 C v2 …C vK ].

3. The multi-objective optimization method for silicon-aluminum alloy turning process parameters based on the improved BPNN-DE algorithm according to claim 2, characterized in that, Step S2 specifically includes the following steps: Step S21: Combine K training sets C t1 C t2 …C tK Train BPNN models separately to obtain K BPNN models M1, M2...M K ; Step S22: From K training sets C t1 C t2 …C tK Select any training set and train the BPNN model M1. Step S23: Let the selected training set data be x = [x1, x2, ... x2]. t ], y = [y1, y2…y t ], t represents the number of training set data, y t Indicates the corresponding x t The tag value; Step S24: Randomly initialize the initial weight matrix w connecting the input layer neurons to the hidden layer neurons. (ih) : in, n represents the number of neurons in the input layer; m represents the number of neurons in the hidden layer; This represents the connection weight between the nth input layer neuron and the mth hidden layer neuron; Step S25: Randomly initialize the bias values ​​b for the connections between the input layer neurons and the hidden layer neurons. (ih) ; Step S26: Randomly initialize the initial weight matrix w connecting the hidden layer neurons to the output layer neurons. (ho) : in, l represents the number of neurons in the output layer; This represents the connection weight between the m-th hidden layer neuron and the l-th output layer neuron; Step S27: Randomly initialize the bias values ​​b of the hidden layer neurons connecting to the output layer neurons. (ho) ; Step S28: Set the hidden layer activation function to Step S29: Calculate the hidden layer output: Out h =f(w (ih) ·x+b (ih) ) in, Out hm This represents the output value of the m-th hidden layer neuron; Step S210: Calculate the output of the output layer: Out o =f(w (ho) ·Out h +b (ho) ) in, Out ol This represents the output value of the l-th output layer neuron; Step S211: Calculate the loss function: Among them, y i This represents the value of the i-th label; Step S212: Calculate the error factor δ0 between the output layer and the hidden layer: Step S213: Update the weights w between the hidden layer and the output layer. (ho) With bias b (ho) : in, This represents the updated weights between the hidden layer and the output layer; This indicates the offset between the updated hidden layer and the output layer; η represents the learning rate, where η > 0; Step S214: Calculate the error factor δ between the input layer and the hidden layer. i : Step S215: Update the weights w between the input layer and the hidden layer. (ih) With bias b (ih) : in, This represents the updated weights between the input layer and the hidden layer; This indicates the bias between the updated input layer and the hidden layer; η represents the learning rate, where η > 0; Step S216: Repeat steps S26 to S212 n times, n>0 times, until the training error Loss value is less than the specified error threshold E, and finally obtain the BPNN model M1; Step S217: Repeat steps S21 to S213 K, K>1 times until all K training sets have been trained once, resulting in the BPNN model set M = [M1, M2, ..., M]. K ]; Step S218: Using test set C v =[C v1 C v2 …C vK The test BPNN model set M = [M1, M2, ..., M] K The fitting accuracy A c =[A c1 A c2 …A cK ] The formula for calculating the model fitting accuracy is: Step S219: Select the model with the highest model fit as the multi-objective optimization model M. A .

4. The multi-objective optimization method for silicon-aluminum alloy turning process parameters based on the improved BPNN-DE algorithm according to claim 3, characterized in that, Step S3 specifically includes the following steps: Step S31: Initialize the parameters of the improved differential evolution model as follows: N p =s Ch=r XOVR = q MAXGEN = k F = t Encoding = RI where, N p =s indicates that the population size is s, s>0; Ch = r indicates that the number of genes in each individual in the population is r, r > 0; The mutation probability is XOVR = q means that the recombination probability is q, 0 < q < 1; MAXGEN = k indicates that the maximum number of generations is k, where k > 0; F = t indicates that the differential scaling factor is t, 0 < t < 1; Encoding=RI indicates that the encoding method uses the real integer RI; Step S32: Define the parent population: z=[z1,z2…z p …With s ] in, z represents the parent population; z p This represents the p-th individual in the parent population, where 1 ≤ p ≤ s. z s This represents the last s-th individual in the parent population; Step S33: Instantiate the parent population using the Gaussian chaotic mapping method: in, express Let p represent the p-th, 1≤p≤s individual in the parent population after Gaussian chaotic mapping; This represents the last s-th individual in the parent population after Gaussian chaotic mapping; z + This represents the parent population after Gaussian chaotic mapping; Step S34: Based on the elite replication selection strategy, select elite individuals from the parent population and directly introduce them into the offspring population. The remaining individuals undergo selection, crossover, and mutation operations. The specific method is as follows: Step S341: Calculate the parent fitness value: in, M represents the BPNN model with the highest fitting accuracy; Represents the set of fitness values ​​of parent individuals; This indicates that individuals are sorted in descending order of their fitness values, from best to worst. Optimal; Step S342: Select Corresponding individual Directly transmitted to the offspring population z c ; Step S35: Introduce the Gaussian mutation process: in, rand represents a random number that follows a uniform distribution between (0,1); N(0,1) represents a standard Gaussian distribution with a mean of 0 and a variance of 1; Let p represent the p-th individual (1≤p≤s) in the population after Gaussian mutation. This represents the population after Gaussian mutation. F represents the differential scaling factor; Indicates from Randomly selected Individuals are not equal; This represents the p-th, 1≤p≤s individual in the population after differencing; This represents the population after differentiation; Step S36: Perform binomial distribution crossover by combining the Gaussian variant population with the parent population: in, This represents the p-th (1≤p≤s) individual in the population after crossover; This represents the population after crossover; Step S37: Implement a one-to-one survival selection strategy to obtain a new generation of subpopulation z. c With c =[z c1 ,With c2 …With cp …With cs ] in, This represents the fitness value of the p-th (1≤p≤s) individual in the population after crossover; This represents the fitness value of the p-th (1≤p≤s) individual in the parent population after Gaussian chaos. z c Indicates the offspring population; z cp This represents the p-th (1≤p≤s) individual in the offspring population; z cs This represents the s-th last individual in the offspring population; Step S38: Use offspring population z c Repeat steps S34 to S37 as the parent population until the set number of generations n, and take the individual with the best fitness value among all individuals in n generations as the individual with the best process parameters. Step S39: Assume there are K (K = b + v) objectives in total, b of which are minimized and v of which are maximized. Optimize each of the K objectives individually using steps S31 to S38 to obtain the minimum value β and the maximum value γ of each objective, which will be used by the multi-objective optimization model to calculate the fitness function in the following steps. Step S310: Optimize the multi-objective model M A Calculate the performance index η of each output value. h η j ; For the minimization objective, the performance metric is expressed as: in, β h Let be the minimum value of the h-th minimization objective; γ h Let be the maximum value of the h-th minimized objective; M Ah (X) represents model M A The value of the h-th minimized objective in the output values; η h =[η1,η2,…,η b ] represents the set of indices for b minimization problems; For the maximization problem, the performance metric is expressed as: in, β j Let be the minimum value of the j-th maximized objective; γ j Let be the maximum value of the j-th maximization objective; M Aj (X) represents model M A The j-th maximized value in the output; η j =[η1,η2,…,η v [] represents the set of indices for v maximization problems; Step S311: Use the geometric mean of all target performance indicators as the total indicator η. When η is larger and tends to 1, it indicates that the input model M A The better the individual in the population, the worse the individual is as η becomes smaller and approaches 0; Step S312: Repeat steps S31 to S38, replacing the formula for calculating the parent fitness value in step S341 with the formula in step S311. The individual with the closest η value to 1 in n generations is selected as the individual with the optimal process parameters.

Images