CN118246527B

CN118246527B - A method and system for predicting quality of abrasive jet cold cutting

Info

Publication number: CN118246527B
Application number: CN202410209518.XA
Authority: CN
Inventors: 武光华; 周文喆; 靳天宇; 孙喜瑞; 张庆芳
Original assignee: Jilin Teachers Institute of Engineering and Technology
Current assignee: Jilin Teachers Institute of Engineering and Technology
Priority date: 2024-02-26
Filing date: 2024-02-26
Publication date: 2024-11-15
Anticipated expiration: 2044-02-26
Also published as: CN118246527A

Abstract

The invention provides a method and a system for predicting abrasive jet cold cutting quality, and belongs to the technical field of abrasive jet prediction. Firstly, collecting cutting experiment data; secondly, carrying out normalization processing on the experimental data, and dividing the experimental data into a training set and a testing set; then constructing a radial basis function neural network model; then optimizing radial basis function neural network model parameters by using a genetic algorithm; finally, evaluating the prediction performance of the radial basis function neural network model by using a test set, and calculating the error between the predicted value and the actual value; judging whether the error accords with an error range, and if so, outputting a radial basis function neural network model; if the error range is not met, retraining the radial basis function neural network model. The invention adopts the radial basis function neural network model and the genetic algorithm, can effectively simulate the nonlinear relation in the abrasive jet cold cutting process, and improves the accuracy and stability of cutting quality prediction.

Description

Abrasive jet flow cold cutting quality prediction method and system

Technical Field

The invention belongs to the technical field of abrasive jet prediction, and particularly relates to a method and a system for predicting abrasive jet cold cutting quality.

Background

Abrasive jet cold cutting is a technique for cutting various materials by utilizing a liquid-solid two-phase jet in which abrasive particles are mixed in a high-pressure water jet. The abrasive jet cold cutting has the advantages of low cutting temperature, high cutting precision, wide cutting range, small environmental pollution and the like, and is widely applied to the fields of industry, ocean engineering, aerospace and the like. However, the quality of the abrasive jet cold cut is affected by a number of factors, such as the cutting process parameters, the abrasive particle characteristics, the properties of the material being cut, etc.

At present, two main methods for predicting the cold cutting quality of abrasive jet flow are: a physical model-based approach and a data-driven based approach. The method based on the physical model is to establish a mathematical model according to the physical mechanism of abrasive jet cold cutting, and obtain the predicted value of cutting quality by solving the equation of the model. The method has the advantages of reflecting the intrinsic law of abrasive jet cold cutting, but also has the disadvantages of complex model building process, difficult model parameter determination, long model solving time consumption and the like. The method based on data driving is to build a data model according to experimental data of abrasive jet cold cutting by utilizing technologies such as machine learning, artificial intelligence and the like, and obtain a predicted value of cutting quality by training parameters of the model. The method has the advantages of being capable of rapidly and accurately predicting the cutting quality, but also has the defects of poor generalization capability of the model, low interpretation of the model, poor stability of the model and the like. Thus, there is a need to develop a method of abrasive jet cold cutting prediction that combines physical mechanisms with data driving.

Disclosure of Invention

Based on the technical problems, the invention provides a method and a system for predicting the cold cutting quality of abrasive jet, and aims to accurately predict and optimize the cutting quality by collecting cutting experimental data and based on a neural network model and a genetic algorithm.

The invention provides a method for predicting the cold cutting quality of abrasive jet, which comprises the following steps:

step S1: collecting cutting experiment data; the experimental data comprise cutting process parameters and cutting processing quality indexes;

Step S2: carrying out normalization processing on the experimental data, and dividing the experimental data into a training set and a testing set;

Step S3: constructing a radial basis function neural network model; the radial basis function neural network model input layer is a cutting process parameter, the output layer is a cutting processing quality index, the activation function is a Gaussian function and the loss function is a mean square error;

Step S4: optimizing radial basis function neural network model parameters by using a genetic algorithm; the parameters comprise the number of hidden layer neurons, a center vector, a width, a connection weight and bias;

Step S5: evaluating the prediction performance of the radial basis function neural network model by using a test set, and calculating an error between a predicted value and an actual value; judging whether the error accords with an error range, and if so, outputting a radial basis function neural network model; if the error range is not met, retraining the radial basis function neural network model.

Optionally, the collecting the cutting experiment data specifically includes:

The cross-sectional area a of the abrasive jet is expressed as:

Wherein d is the nozzle diameter; alpha is the half apex angle of the jet; l is the target distance;

The velocity V of the abrasive jet is expressed as:

wherein Q is the abrasive jet flow; v is jet velocity;

The kinetic energy E _k of the jet is expressed as:

Wherein E _k is the kinetic energy of abrasive jet flow; ρ is the abrasive jet density;

the pressure P of the jet is expressed as:

Wherein P is abrasive jet pressure;

The impact force F of the jet is expressed as:

Wherein F is the impact force of abrasive jet; θ is the angle between the axis and the surface of the cut material;

The loss level LR is expressed as:

Wherein LR is loss degree; m _s is the mass of the sample after cutting; m _a is the mass of abrasive material consumed from the nozzle during cutting; m _n is the mass of the nozzle worn during cutting; ρ _a is the abrasive density; ρ _n is the nozzle density; t is cutting time; the E is the wear coefficient of the nozzle; m ₀ is the mass of the material before cutting, m ₀＝m_s+m_a+m_n;

The energy consumption EC is expressed as:

Wherein EC is energy consumption; w _e is the electric energy consumed in the cutting process; w _w is water energy consumed in the cutting process, and eta _e is electric energy conversion efficiency; ρ _w is the density of water; c _w is the specific heat capacity of water; delta T is the temperature rise of water;

the cutting accuracy CP is expressed as:

In the formula, CP is cutting precision, and refers to similarity between a cut after cutting and an expected cut; Δl is the deviation of the cut length from the expected length after cutting; Δw is the deviation of the cut width from the intended width after cutting; r _a is the kerf surface roughness after dicing.

Optionally, the normalizing the experimental data specifically includes:

wherein N is the number of experimental data; x is a cutting process parameter matrix; y is a cutting processing quality index matrix;

Data normalization is expressed as:

Wherein, x _ij and y _ij are respectively the cutting process parameter and the cutting processing quality index of the ith sample; x _ij 'and y _ij' are respectively the cutting process parameter and the cutting processing quality index of the ith sample after normalization; x _j and y _j are the cutting process parameter and the cutting quality index of the j-th column respectively; min (x _j) and max (x _j) are the minimum and maximum values, respectively, of the cutting process parameters of the j-th column; min (y _j) and max (y _j) represent the minimum and maximum values of the cutting quality index of the j-th column, respectively.

Optionally, the constructing a radial basis function neural network model specifically includes:

The radial basis function neural network model input layer is a cutting process parameter; the output layer is a cutting processing quality index; the number of neurons of the hidden layer is M;

the activation function of the hidden layer is expressed as:

Wherein x is the data of the input layer, namely the normalized cutting process parameters; c _I is the center vector of the I-th hidden layer neuron; σ _I is the width parameter of the I-th hidden layer neuron; phi is a radial basis function, i.e., a Gaussian function; the term "I". I "is the Euclidean norm;

The output function of the output layer is expressed as:

Wherein y _J (x) is the output value of the neuron of the J-th output layer, namely the normalized cutting processing quality index; w _IJ is the connection weight of the I-th hidden layer neuron to the J-th output layer neuron; b _J is the bias of the J-th output layer neuron;

the loss function is expressed as:

Wherein y _kJ is the actual value of the J-th cutting quality index of the k-th sample; A predicted value of a J-th cut quality index for a k-th sample; the number of training set samples, i.e., the number of portions of experimental data.

Optionally, the optimizing the radial basis function neural network model parameter by using a genetic algorithm specifically comprises:

initializing parameters, namely setting population scale as S, maximum evolution algebra as G _max, initial crossover probability as P _c, initial mutation probability as P _m, elite individual number as E, current algebra as g=0, upper limit of hidden layer neuron number as M _max, value range of central vector and width parameter as [0,1], and value range of connection weight and bias as [ -1,1];

Generating an initial population, randomly generating S individuals, wherein each individual consists of the number M of hidden layer neurons, a central vector C= [ C ₁,c₂,...,c_M ], a width parameter sigma= [ sigma ₁,σ₂,…,σ_M ], a connection weight W= [ W ₁₁,w₁₂,…,w_M3 ] and a bias B= [ B ₁,b₂,b₃ ], and the expression is as follows:

X_s＝[M，C，∑，W，B]，s＝1，2，…，S

wherein X _s is the s-th individual; m is an integer, and M is more than or equal to 1 and less than or equal to M _max; C. sigma, W and B are real vectors, and satisfy 0.ltoreq.C, sigma.ltoreq.1, -1.ltoreq.W, B.ltoreq.1;

Fitness is calculated, for each individual X _s, an RBF neural network is constructed from its parameters, its Loss function Loss _s is calculated using a training set, and then it is converted into fitness function F _s, expressed as:

wherein iota is a small positive number for avoiding zero denominator;

selecting S individuals to enter the next generation by using a roulette method, and reserving E elite individuals with highest fitness, namely E individuals not participating in crossing and mutation operations, and directly copying to the next generation;

crossover operation, using adaptive crossover probabilities, is expressed as:

Wherein P _c,s is the s-th individual crossover probability; g is the current algebra; g _max is the maximum algebra;

For each pair of adjacent individuals, performing crossover operation according to crossover probability, namely exchanging part or all parameters, and generating two new individuals, wherein the method specifically comprises the following steps:

the intersection of the hidden layer neuron numbers M randomly selects one intersection p, and then swaps the first p-bit binary codes of M of two individuals to generate two new M values, expressed as:

M′₁＝M₁[1：p]+M₂[p+1：M_max]

M′₂＝M₂[1：p]+M₁[p+1：M_max]

Wherein M ₁ and M ₂ are the original M values of two individuals; m '₁ and M' ₂ are new M values for two individuals; m [ l: ζ represents the binary encoding of the first to ζ bits of M; satisfy p is more than or equal to 1M _max -1 or less;

The intersection of the center vectors C randomly selects one intersection point a, then swaps the first a elements of the two individual C, generating two new C vectors, denoted as:

wherein, C '₁ and C' ₂ are new C vectors for two individuals; c _sβ represents the B-th center vector element of the s-th individual; a is more than or equal to 1 and less than or equal to M _min;M_min and M _mm＝min(M′₁,M′₂);

intersection of the width parameters sigma, randomly selecting one intersection r, then exchanging the first r elements of the two individual sigma, generating two new sigma vectors, denoted as:

Where Σ '₁ and Σ' ₂ are the new Σ vectors of two individuals; σ _sγ represents the gamma-th center vector element of the s-th individual; r is more than or equal to 1 and less than or equal to M _min;

the intersection of the connection weights W randomly selects one intersection f, and then swaps the first f elements of W of two individuals, generating two new W vectors, expressed as:

Wherein W '₁ and W' ₂ are new W vectors for two individuals; w _sIJ is the connection weight of the ith hidden layer neuron to the jth output layer neuron representing the s-th individual; f is more than or equal to 1 and less than or equal to 3M _min;

Offset B's intersection, randomly selecting one intersection h, then exchanging the first h elements of B for two individuals, generating two new B vectors, expressed as:

B′₁＝[b₁₁,b₁₂,…,b_1h,b_2h+1,b_2h+2,…,b₂₃]

B′₂＝[b₂₁,b₂₂,…,b_2h,b_1h+1,b_1h+2,…,b₁₃]

Wherein B '₁ and B' ₂ are new B vectors for two individuals; b _sJ is the bias of the J-th output layer neuron representing the s-th individual; h is more than or equal to 1 and less than or equal to 3;

A mutation operation, using an adaptive mutation probability, expressed as:

Wherein P _m,s is the probability of variation of the s-th individual; g is the current algebra; g _max is the maximum algebra;

For each individual, performing mutation operation according to mutation probability, namely performing tiny disturbance on part or all parameters to generate a new individual, wherein the method specifically comprises the following steps:

The variation of the hidden layer neuron number M randomly selects one cross point o, and then the binary code of the o bit is turned over to generate a new M value, which is expressed as:

M′＝M[1：o-1]+M[o]+M[o+1：M_max]

Wherein M' is a new M value; m [ o ] represents the inverse of the binary encoding of the o-th bit of M, i.e., 0 becomes 1 and 1 becomes 0; satisfying the condition that o is more than or equal to 1 and less than or equal to M _max;

The variation of the center vector C randomly selects a cross point u, and then adds a random number which obeys normal distribution to the u-th element to generate a new C vector expressed as:

C′＝[c₁,c₂,…,c_u+δ,…,c_M′]

Wherein, C' is a new C vector; delta is a random number which obeys normal distribution N (0, sigma _c); σ _c is a small standard deviation for controlling the amplitude of the variation; satisfying the condition that o is more than or equal to 1 and less than or equal to M';

variation of the width parameter sigma, randomly selecting a cross point r, and then adding a random number compliant with a normal distribution to the r-th element to generate a new sigma vector expressed as:

∑′＝[σ₁,σ₂,…,σ_r+δ,…,σ_M′]

Wherein, sigma' is a new Sigma vector; delta is a random number which obeys normal distribution N (0, sigma _σ); σ _σ is a small standard deviation for controlling the amplitude of the variation; satisfying r is more than or equal to 1 and less than or equal to M';

the variation of the connection weight W randomly selects a variation point v, then adds a random number which is compliant with normal distribution to the v-th element to generate a new W vector, which is expressed as:

W′＝[w₁₁,w₁₂,…,w_v+δ,…,w_3M′]

Wherein W' is a new W vector; delta is a random number conforming to normal distribution N (0, sigma _w), sigma _w is a smaller standard deviation for controlling the amplitude of variation; satisfy v of 1 to less than or equal to v not more than 3M';

bias B variation, randomly selecting a variation point z, and then adding a random number compliant with normal distribution to the z-th element to generate a new B vector expressed as:

B′＝[b₁,b₂,…,b_z+δ,…,b₃]

wherein B' is a new B vector; delta is a random number conforming to normal distribution N (0, sigma _b), sigma _b is a smaller standard deviation for controlling the amplitude of variation; satisfying z is more than or equal to 1 and less than or equal to 3;

stopping evolution if the maximum evolution algebra G _max is reached or the adaptability change of the population is smaller than a set threshold value, and outputting the parameters and the adaptability of the optimal individual and the corresponding radial basis function neural network model; otherwise, let g=g+1, return to calculate fitness, continue evolution.

The invention also provides an abrasive jet cold cutting quality prediction system, which comprises:

The experimental data collection module is used for collecting cutting experimental data; the experimental data comprise cutting process parameters and cutting processing quality indexes;

The normalization processing dividing module is used for carrying out normalization processing on the experimental data and dividing the experimental data into a training set and a testing set;

The radial basis function network construction module is used for constructing a radial basis function network model; the radial basis function neural network model input layer is a cutting process parameter, the output layer is a cutting processing quality index, the activation function is a Gaussian function and the loss function is a mean square error;

The network parameter optimization module is used for optimizing radial basis function neural network model parameters by using a genetic algorithm; the parameters comprise the number of hidden layer neurons, a center vector, a width, a connection weight and bias;

The model performance evaluation module is used for evaluating the prediction performance of the radial basis function neural network model by using the test set and calculating the error between the prediction value and the actual value; judging whether the error accords with an error range, and if so, outputting a radial basis function neural network model; if the error range is not met, retraining the radial basis function neural network model.

Optionally, the experimental data collection module specifically includes:

The cross-sectional area a of the abrasive jet is expressed as:

The velocity V of the abrasive jet is expressed as:

wherein Q is the abrasive jet flow; v is jet velocity;

The kinetic energy E _k of the jet is expressed as:

the pressure P of the jet is expressed as:

Wherein P is abrasive jet pressure;

The impact force F of the jet is expressed as:

The loss level LR is expressed as:

The energy consumption EC is expressed as:

the cutting accuracy CP is expressed as:

Optionally, the normalization processing dividing module specifically includes:

Data normalization is expressed as:

Wherein, x _ij and y _ij are respectively the cutting process parameter and the cutting processing quality index of the ith sample; x '_ij and y' _ij are respectively the cutting process parameter and the cutting processing quality index of the ith sample after normalization; x _j and y _j are the cutting process parameter and the cutting quality index of the j-th column respectively; min (x _j) and max (x _j) are the minimum and maximum values, respectively, of the cutting process parameters of the j-th column; min (y _j) and max (y _j) represent the minimum and maximum values of the cutting quality index of the j-th column, respectively.

Optionally, the radial base network construction module specifically includes:

the activation function of the hidden layer is expressed as:

The output function of the output layer is expressed as:

the loss function is expressed as:

Optionally, the network parameter optimization module specifically includes:

The parameter initialization submodule is used for initializing parameters, setting population scale as S, maximum evolution algebra as G _max, initial crossover probability as P _c, initial mutation probability as P _m, elite individual number as E, current algebra as g=0, upper limit of hidden layer neuron number as M _max, value range of central vector and width parameter as [0,1], and value range of connection weight and bias as [ -1,1];

The initial population generation sub-module is used for generating an initial population, randomly generating S individuals, wherein each individual consists of the number M of hidden layer neurons, a center vector C= [ C ₁,c₂,...,c_M ], a width parameter sigma= [ sigma ₁,σ₂,…,σ_M ], a connection weight W= [ W ₁₁,w₁₂,…,w_M3 ] and a bias B= [ B ₁,b₂,b₃ ], and the expression is as follows:

X_s＝[M，C，∑，W，B]，s＝1，2，…，S

The fitness calculation sub-module is used for calculating fitness, for each individual X _s, constructing RBF neural network according to parameters thereof, calculating a Loss function Loss _s by using a training set, and then converting the Loss function Loss _s into a fitness function F _s, wherein the fitness function F _s is expressed as:

wherein iota is a small positive number for avoiding zero denominator;

The selection sub-module is used for performing selection operation, selecting S individuals to enter the next generation by using a roulette method, and simultaneously reserving E elite individuals, namely E individuals with highest fitness, which do not participate in crossover and mutation operation and are directly copied to the next generation;

the cross submodule is used for performing cross operation, and the adaptive cross probability is used and expressed as:

M′₁＝M₁[1：p]+M₂[p+1：M_max]

M′₂＝M₂[1：p]+M₁[p+1：M_max]

Wherein, C '₁ and C' ₂ are new C vectors for two individuals; c _sβ represents the B-th center vector element of the s-th individual; a is more than or equal to 1 and less than or equal to M _min;M_min and M _min＝min(M′₁,M′₂);

B′₁＝[b₁₁,b₁₂,…,b_1h,b_2h+1,b_2h+2,…,b₂₃]

B′₂＝[b₂₁,b₂₂,…,b_2h,b_1h+1,b_1h+2,…,b₁₃]

the mutation submodule is used for performing mutation operation, and the adaptive mutation probability is used for representing as:

M′＝M[1：o-1]+M[o]+M[o+1：M_max]

C′＝[c₁,c₂,…,c_u+δ,…,c_M′]

∑′＝[σ₁,σ₂,…,σ_r+δ,…,σ_M′]

W′＝[w₁₁,w₁₂,…,w_v+δ,…,w_3M′]

B′＝[b₁,b₂,…,b_z+δ,…,b₃]

the condition termination submodule is used for terminating the condition, and if the maximum evolution algebra G _max is reached or the adaptability change of the population is smaller than a set threshold value, stopping the evolution, and outputting the parameters and the adaptability of the optimal individual and the corresponding radial basis neural network model; otherwise, let g=g+1, return to calculate fitness, continue evolution.

Compared with the prior art, the invention has the following beneficial effects:

According to the invention, a Radial Basis Function (RBF) neural network is adopted as a data model, so that nonlinear, high-dimensional and complex data relationships can be effectively fitted, and the prediction accuracy of the cutting quality is improved; genetic (GA) is adopted as an optimization algorithm, so that a local optimal solution can be effectively avoided, a global optimal solution is searched, and generalization capability and stability of the model are improved; by adopting normalization processing and error range judgment, the dimension and scale influence of data can be effectively eliminated, and the reliability and the robustness of the model are improved;

drawings

FIG. 1 is a flow chart of a method for predicting the cold cutting quality of abrasive jet according to the present invention;

FIG. 2 is a block diagram of an abrasive jet cold cutting quality prediction system according to the present invention.

Detailed Description

The invention is further described below in connection with specific embodiments and the accompanying drawings, but the invention is not limited to these embodiments.

Example 1

As shown in fig. 1, the invention discloses a method for predicting the cold cutting quality of abrasive jet, which comprises the following steps:

Step S1: collecting cutting experiment data; the experimental data includes cutting process parameters and cutting quality indicators.

Step S2: and carrying out normalization processing on experimental data, and dividing the experimental data into a training set and a testing set.

Step S3: constructing a radial basis function neural network model; the radial basis function neural network model has an input layer of cutting process parameters, an output layer of cutting processing quality indexes, an activation function of a Gaussian function and a loss function of a mean square error.

Step S4: optimizing radial basis function neural network parameters using a genetic algorithm; parameters include hidden layer neuron number, center vector, width, connection weight, and bias.

Step S5: evaluating the prediction performance of the radial basis function neural network by using a test set, and calculating an error between a predicted value and an actual value; judging whether the error accords with the error range, and if so, outputting a radial basis function neural network model; if the error range is not met, retraining the radial basis function network.

The steps are discussed in detail below:

The step S1 specifically comprises the following steps:

In the abrasive jet structure, the jet is conical, the vertex of the jet is positioned at the outlet of the nozzle, the half vertex angle of the jet is alpha, and the included angle between the axis of the jet and the surface of the material to be cut is theta.

The cross-sectional area a of the abrasive jet is expressed as:

wherein d is the nozzle diameter; this formula shows that the cross-sectional area of the jet increases with increasing target distance, but the rate of increase decreases with increasing target distance; when the target distance is zero, the cross-sectional area of the jet is equal to the cross-sectional area of the nozzle, i.e. a=pi d ²/4; when the target distance tends to be infinitely large, the sectional area of the jet flow tends to be infinite, that is, A.fwdarw.infinity.

The velocity V of the abrasive jet is expressed as:

wherein Q is the abrasive jet flow; v is jet velocity.

The kinetic energy E _k of the jet is expressed as:

wherein E _k is the kinetic energy of abrasive jet flow; m is abrasive jet mass; ρ is the abrasive jet density.

The pressure P of the jet is expressed as:

Wherein P is the abrasive jet pressure.

The impact force F of the jet is expressed as:

wherein F is the impact force of abrasive jet.

The loss level LR is expressed as:

Wherein LR is loss degree; m _s is the mass of the sample after cutting; m _a is the mass of abrasive material consumed from the nozzle during cutting; m _n is the mass of the nozzle worn during cutting; ρ _a is the abrasive density; ρ _n is the nozzle density; t is cutting time; the E is the wear coefficient of the nozzle; m ₀ is the mass of the material before cutting, m ₀＝m_s+m_a+m_n.

The energy consumption EC is expressed as:

Wherein EC is energy consumption; w _e is the electric energy consumed in the cutting process; w _w is water energy consumed in the cutting process, and eta _e is electric energy conversion efficiency; ρ _w is the density of water; c _w is the specific heat capacity of water; delta T is the temperature rise of water.

The cutting accuracy CP is expressed as:

In the formula, CP is cutting precision, and refers to similarity between a cut after cutting and an expected cut; Δl is the deviation of the cut length from the expected length after cutting; Δw is the deviation of the cut width from the intended width after cutting; r _a is the surface roughness of the cut; f is the jet impact force of the abrasive; alpha is the half apex angle of the jet; d is the particle size of the abrasive; d is the nozzle diameter; v is jet velocity; l is the target distance.

In the embodiment, the cutting process parameters comprise jet pressure P, abrasive flow Q, abrasive grain diameter D, nozzle diameter D, jet speed V, target distance L, abrasive jet impact force F, jet half-apex angle alpha, cutting included angle theta and the like; the cutting quality index includes the degree of loss, energy consumption and cutting accuracy.

The step S2 specifically comprises the following steps:

wherein N is the number of experimental data; x is a cutting process parameter matrix; y is a cutting processing quality index matrix.

Data normalization is expressed as:

The division into training and testing sets is to enable Radial Basis (RBF) neural networks and Genetic (GA) algorithms to learn and optimize on one part of the data and evaluate and verify on another part of the data. Generally, the training set accounts for a large portion of the data and the test set accounts for a small portion of the data; the specific ratio is determined according to the data amount and the demand.

The step S3 specifically comprises the following steps:

Constructing a radial basis function neural network model (RBF), wherein an input layer of the radial basis function neural network model is a cutting process parameter, and nine neurons are arranged, wherein the nine neurons comprise jet pressure P, abrasive flow Q, abrasive grain diameter D, nozzle diameter D, jet speed V, target distance L, abrasive jet impact force F, jet half-apex angle a, cutting included angle theta and the like; the neuron of the input layer is specifically set in combination with the actual situation; the output layer is a cutting processing quality index, and three neurons are arranged and respectively correspond to the three cutting processing quality indexes; the number of neurons of the hidden layer is M, and can be determined through GA algorithm optimization.

The activation function of the hidden layer is a gaussian function, expressed as:

Wherein x is the data of the input layer, namely the normalized cutting process parameters; c _I is the center vector of the I-th hidden layer neuron; σ _I is the width parameter of the I-th hidden layer neuron; phi is a radial basis function, i.e., a Gaussian function; the term "I". I "is the Euclidean norm.

The output function of the output layer is a linear function, expressed as:

Wherein y _J (x) is the output value of the neuron of the J-th output layer, namely the normalized cutting processing quality index; w _IJ is the connection weight of the I-th hidden layer neuron to the J-th output layer neuron; b _J is the bias of the J-th output layer neuron.

The loss function is the mean square error, expressed as:

Wherein y _kJ is the actual value of the J-th cutting quality index of the k-th sample; A predicted value of a J-th cut quality index for a k-th sample; the training set sample number is part of experimental data; the goal is to minimize the Loss function Loss by optimizing the parameters of the RBF neural network.

Step S4: optimizing parameters of the radial basis function neural network using an improved genetic algorithm; parameters include hidden layer neuron number, center vector, width, connection weight, and bias.

The step S4 specifically comprises the following steps:

Initializing parameters, setting population scale as S, maximum evolution algebra as G _max, initial crossover probability as P _c, initial mutation probability as P _m, elite individual number as E, current algebra as g=0, upper limit of hidden layer neuron number as M _max, value range of central vector and width parameters as [0,1], and value range of connection weight and bias as [ 1,1].

X_s＝[M，C，∑，W，B]，s＝1，2，…，S

Wherein X _s is the s-th individual; m is an integer, and M is more than or equal to 1 and less than or equal to M _max; C. sigma, W and B are real vectors, and satisfy 0.ltoreq.C, sigma.ltoreq.1, -1.ltoreq.W, and B.ltoreq.1.

wherein iota is a small positive number for avoiding zero denominator; the larger the fitness function, the higher the quality of the individual.

And selecting S individuals to enter the next generation by using a roulette method, and simultaneously reserving E elite individuals, namely E individuals with highest fitness, without participating in crossing and mutation operations, and directly copying to the next generation.

Crossover operation, using adaptive crossover probabilities, is expressed as:

Wherein P _c,s is the s-th individual crossover probability; g is the current algebra; g _max is the maximum algebra.

The adaptive crossover probability decreases as the algebra increases to maintain population diversity. For each pair of adjacent individuals, performing crossover operation according to crossover probability, namely exchanging part or all parameters, and generating two new individuals, wherein the method specifically comprises the following steps:

I. Crossover of hidden layer neuron number M: one intersection p is randomly selected and then the first p bits of binary codes of the two individual M are swapped to generate two new M values, expressed as:

M′₁＝M₁[1：p]+M₂[p+1：M_max]

M′₂＝M₂[1：p]+M₁[p+1：M_max]

Wherein M ₁ and M ₂ are the original M values of two individuals; m '₁ and M' ₂ are new M values for two individuals; m [ l: ζ represents the binary encoding of the first to ζ bits of M; satisfy p is more than or equal to 1M _max -1 is not more than.

II. Intersection of center vector C: one intersection a is randomly selected and then the first a elements of the two individual cs are swapped to generate two new C vectors, expressed as:

wherein, C '₁ and C' ₂ are new C vectors for two individuals; c _sβ represents the β center vector element of the s-th individual; a is more than or equal to 1 and less than or equal to M _min;M_min and M _min＝min(M′₁,M′₂).

III, crossing of width parameter Σ: one intersection r is randomly selected and then the first r elements of the sigma of the two individuals are exchanged, generating two new sigma vectors, denoted:

Where Σ '₁ and Σ' ₂ are the new Σ vectors of two individuals; σ _sγ represents the gamma-th center vector element of the s-th individual; r is more than or equal to 1 and less than or equal to M _min.

IV, crossing of connection weights W: one intersection f is randomly selected and then the first f elements of the W of the two individuals are swapped to generate two new W vectors, expressed as:

Wherein W '₁ and W' ₂ are new W vectors for two individuals; w _sIJ is the connection weight of the ith hidden layer neuron to the jth output layer neuron representing the s-th individual; f is more than or equal to 1 and less than or equal to 3M _min.

V, crossing of bias B: one intersection h is randomly selected and then the first h elements of B of two individuals are swapped to generate two new B vectors, expressed as:

B′₁＝[b₁₁,b₁₂,…,b_1h,b_2h+1,b_2h+2,…,b₂₃]

B′₂＝[b₂₁,b₂₂,…,b_2h,b_1h+1,b_1h+2,…,b₁₃]

Wherein B '₁ and B' ₂ are new B vectors for two individuals; b _sJ is the bias of the J-th output layer neuron representing the s-th individual; h is more than or equal to 1 and less than or equal to 3.

A mutation operation, using an adaptive mutation probability, expressed as:

wherein P _m,s is the probability of variation of the s-th individual; g is the current algebra; g _max is the maximum algebra.

The probability of adaptive mutation decreases with increasing algebra to maintain diversity of the population. For each individual, performing mutation operation according to mutation probability, namely performing tiny disturbance on part or all parameters to generate a new individual, wherein the method specifically comprises the following steps:

(1) Variation of the number M of hidden neurons: randomly selecting a cross point o, and then turning over the binary code of the o-th bit to generate a new M value, which is expressed as:

M′＝M[1：o-1]+M[o]+M[o+1：M_max]

Wherein M' is a new M value; m [ o ] represents the inverse of the binary encoding of the o-th bit of M, i.e., 0 becomes 1 and 1 becomes 0; satisfies that o is more than or equal to 1 and less than or equal to M _max.

(2) Variation of center vector C: a cross point u is randomly selected, and then a random number which is subjected to normal distribution is added to the u-th element, so that a new C vector is generated, and the new C vector is expressed as:

C′＝[c₁,c₂,…,c_u+δ,…,c_M′]

wherein, C' is a new C vector; delta is a random number which obeys normal distribution N (0, sigma _c); σ _c is a small standard deviation for controlling the amplitude of the variation; satisfies that o is more than or equal to 1 and less than or equal to M'.

(3) Variation of width parameter Σ: a cross point r is randomly selected, and then a random number which is subjected to normal distribution is added to the r element to generate a new sigma vector, which is expressed as:

∑′＝[σ₁,σ₂,…,σ_r+δ,…,σ_M′]

Wherein, sigma' is a new Sigma vector; delta is a random number which obeys normal distribution N (0, sigma _σ); σ _σ is a small standard deviation for controlling the amplitude of the variation; satisfying r is more than or equal to 1 and less than or equal to M'.

(4) Variation of the connection weight W: randomly selecting a variation point v, then adding a random number which is subjected to normal distribution to the v-th element, and generating a new W vector which is expressed as:

W′＝[w₁₁,w₁₂,…,w_v+δ,…,w_3M′]

wherein W' is a new W vector; delta is a random number conforming to normal distribution N (0, sigma _w), sigma _w is a smaller standard deviation for controlling the amplitude of variation; satisfy v of 1 to less than or equal to v not more than 3M'.

(5) Variation of bias B: randomly selecting a variation point z, and then adding a random number obeying normal distribution to the z-th element to generate a new B vector expressed as:

B′＝[b₁,b₂,…,b_z+δ,…,b₃]

Wherein B' is a new B vector; delta is a random number conforming to normal distribution N (0, sigma _b), sigma _b is a smaller standard deviation for controlling the amplitude of variation; satisfying z is more than or equal to 1 and less than or equal to 3.

If the maximum evolution algebra G _max is reached, or the adaptability change of the population is smaller than a set threshold, or the program is terminated in advance, stopping the evolution, and outputting the parameters and the adaptability of the optimal individual and the corresponding RBF neural network model; otherwise, let g=g+1, return to calculate fitness, continue evolution.

The step S5 specifically comprises the following steps:

Substituting the data of the test set into parameters and fitness of the optimal individual and a corresponding RBF neural network model to obtain a predicted value; performing inverse normalization on the predicted value to obtain an original predicted value, wherein the method specifically comprises the following steps:

Wherein min (y _j) and max (y _j) are the minimum value and the maximum value of the cutting quality index of the j-th column, respectively; Is a predicted value; Is the original predicted value.

Calculating a predicted valueAnd the mean absolute error, root mean square error, and mean absolute percent error between the actual values y _J (x), expressed as:

Wherein MAE _J is the average absolute error of the J-th cutting quality index; RMSE _J is the root mean square error of the J-th cut quality index; MAPE _J is the average absolute percentage error of the J-th cutting quality index; For a test set sample; And y _JA (x) represent the predicted value and the actual value of the J-th cut quality index of the a-th sample, respectively.

The method for judging whether the error meets the requirement by using the weighted comprehensive evaluation method specifically comprises the following steps:

Firstly, setting a threshold value for each error type (average absolute error, root mean square error and average absolute percentage error) respectively, wherein the threshold value represents acceptable error; for each error type of each index, its normalized error relative to the corresponding threshold is then calculated, expressed as:

Wherein E _J,et is the normalized error of the et-th error type of the J-th cutting machining quality index; error _J,et is the actual error of the et-th error type of the J-th cut quality index, error _J,et includes MAE _J、RMSE_J and MAPE _J;threshold_et as thresholds of the et-th error type.

The weighted error is then calculated for each index, expressed as:

wherein Γ _J is the weighted error of the J-th cutting quality index; is the weight of the type of error of the et.

Finally, analyzing the size of each index error gamma _J, if gamma _J meets the expected precision requirement, indicating that the RBF neural network has good prediction performance, is used for the prediction control of the cutting processing quality, and outputs an RBF neural network model; if Γ _J is too large, which indicates that the generalization capability of the RBF neural network is insufficient, parameters or structures of the network need to be adjusted, or the data volume of a training set is increased, and the RBF neural network is retrained.

In this embodiment, the abrasive jet cold cutting robot is adopted to cut subsequently, and the cutting robot is an intelligent cutting device that utilizes robot technique and cutting technique to combine together, and it can accomplish the cutting processing of various shapes and sizes automatically according to different cutting demands, improves cutting efficiency and quality, reduces cutting cost and manpower resources. And sending the cutting technological parameters to a control system of the cutting robot, and controlling the movement of the cutting robot and the work of cutting equipment by the control system according to the parameter instructions to finish cutting processing. In the cutting process, the cutting state is monitored in real time, cutting process parameters are input into the RBF neural network to obtain a real-time predicted value, the real-time predicted value is compared with an expected target value, and a real-time predicted error is calculated. If the prediction error is within the allowable error range, the cutting processing quality is up to the requirement, and the cutting is continued; if the prediction error exceeds the error range, the quality of the cutting processing is unqualified, the parameters of the cutting process are required to be adjusted and then are sent to a control system of the cutting robot, and the movement of the cutting robot and the operation of the cutting equipment are adjusted until the prediction error is within the error range.

Example 2

As shown in fig. 2, the present invention discloses an abrasive jet cold cutting quality prediction system, which comprises:

an experimental data collection module 10 for collecting cutting experimental data; the experimental data includes cutting process parameters and cutting quality indicators.

The normalization processing dividing module 20 is configured to perform normalization processing on the experimental data, and divide the experimental data into a training set and a testing set.

A radial basis network construction module 30 for constructing a radial basis neural network model; the radial basis function neural network model has an input layer of cutting process parameters, an output layer of cutting processing quality indexes, an activation function of a Gaussian function and a loss function of a mean square error.

A network parameter optimization module 40 for optimizing radial basis function neural network model parameters using a genetic algorithm; parameters include hidden layer neuron number, center vector, width, connection weight, and bias.

A model performance evaluation module 50 for evaluating the predicted performance of the radial basis function network model using the test set, calculating an error between the predicted value and the actual value; judging whether the error accords with the error range, and if so, outputting a radial basis function neural network model; if the error range is not met, retraining the radial basis function neural network model.

As an alternative embodiment, the experimental data collection module 10 of the present invention specifically includes:

The cross-sectional area a of the abrasive jet is expressed as:

wherein d is the nozzle diameter; alpha is the half apex angle of the jet; l is the target distance.

The velocity V of the abrasive jet is expressed as:

wherein Q is the abrasive jet flow; v is jet velocity.

The kinetic energy E _k of the jet is expressed as:

wherein E _k is the kinetic energy of abrasive jet flow; ρ is the abrasive jet density.

The pressure P of the jet is expressed as:

Wherein P is the abrasive jet pressure.

The impact force F of the jet is expressed as:

Wherein F is the impact force of abrasive jet; θ is the angle between the axis and the surface of the material being cut.

The loss level LR is expressed as:

Wherein LR is loss degree; m _s is the mass of the sample after cutting; m _a is the mass of abrasive material consumed from the nozzle during cutting; mn is the mass of the nozzle worn during cutting; ρ _a is the abrasive density; ρ _n is the nozzle density; t is cutting time; the E is the wear coefficient of the nozzle; m ₀ is the mass of the material before cutting, m ₀＝m_s+m_a+m_n.

The energy consumption EC is expressed as:

The cutting accuracy CP is expressed as:

As an alternative embodiment, the normalization processing partitioning module 20 of the present invention specifically includes:

Data normalization is expressed as:

Wherein, x _ij and y _ij are respectively the cutting process parameter and the cutting processing quality index of the ith sample; x '_ij and y _ij' are respectively the cutting process parameter and the cutting processing quality index of the ith sample after normalization; x _j and y _j are the cutting process parameter and the cutting quality index of the j-th column respectively; min (x _j) and max (x _j) are the minimum and maximum values, respectively, of the cutting process parameters of the j-th column; min (y _j) and max (y _j) represent the minimum and maximum values of the cutting quality index of the j-th column, respectively.

As an alternative embodiment, the radial base network construction module 30 of the present invention specifically includes:

The radial basis function neural network model input layer is a cutting process parameter; the output layer is a cutting processing quality index; the number of neurons in the hidden layer is M.

The activation function of the hidden layer is expressed as:

The output function of the output layer is expressed as:

The loss function is expressed as:

As an alternative embodiment, the network parameter optimization module 40 of the present invention specifically includes:

The parameter initialization submodule is used for initializing parameters, setting population scale as S, maximum evolution algebra as G _max, initial crossover probability as P _c, initial mutation probability as P _m, elite individual number as B, current algebra as g=0, upper limit of hidden layer neuron number as M _max, value ranges of central vector and width parameters as [0,1], and value ranges of connection weight and bias as [ -1,1].

X_s＝[M，C，∑，W，B]，s＝1，2，…，S

Where iota is a small positive number to avoid zero denominator.

And the selection sub-module is used for performing selection operation, selecting S individuals to enter the next generation by using a roulette method, and simultaneously reserving E elite individuals, namely E individuals with highest fitness, without participating in crossover and mutation operation, and directly copying the E elite individuals to the next generation.

M′₁＝M₁[1：p]+M₂[p+1：M_max]

M′₂＝M₂[1：p]+M₁[p+1：M_max]

wherein, C '₁ and C' ₂ are new C vectors for two individuals; c _sβ represents the B-th center vector element of the s-th individual; a is more than or equal to 1 and less than or equal to M _min;M_min and M _min＝min(M′₁,M′₂).

B′₁＝[b₁₁,b₁₂,…,b_1h,b_2h+1,b_2h+2,…,b₂₃]

B′₂＝[b₂₁,b₂₂,…,b_2h,b_1h+1,b_1h+2,…,b₁₃]

M′＝M[1：o-1]+M[o]+M[o+1：M_max]

C′＝[c₁,c₂,…,c_u+δ,…,c_M′]

∑′＝[σ₁,σ₂,…,σ_r+δ,…,σ_M′]

W′＝[w₁₁,w₁₂,…,w_v+δ,…,w_3M′]

B′＝[b₁,b₂,…,b_z+δ,…,b₃]

The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for predicting the quality of abrasive jet cold cutting, characterized in that the method comprises:

Step S1: Collect cutting experimental data; the experimental data includes cutting process parameters and cutting process quality indicators, specifically including:

The cross-sectional area A of the abrasive jet is expressed as:

Where, d is the nozzle diameter; α is the semi-apex angle of the jet; L is the target distance;

The velocity V of the abrasive jet is expressed as:

Where, Q is the abrasive jet flow rate; V is the jet velocity;

The kinetic energy E _k of the jet is expressed as:

Where, _Ek is the kinetic energy of the abrasive jet; ρ is the density of the abrasive jet;

The pressure P of the jet is expressed as:

Where, P is the abrasive jet pressure;

The impact force F of the jet is expressed as:

Where F is the impact force of the abrasive jet; θ is the angle between the axis and the surface of the material being cut;

The loss level LR is expressed as:

Wherein, LR is the loss degree; _ms is the sample mass after cutting; _ma is the abrasive mass consumed from the nozzle during the cutting process; _mn is the nozzle mass worn during the cutting process; _ρa is the abrasive density; _ρn is the nozzle density; t is the cutting time; ∈ is the nozzle wear coefficient; _m0 is the material mass before cutting, _m0 = _ms +m _a + _mn ;

Energy consumption EC is expressed as:

Where EC is energy consumption; _We is the electrical energy consumed during the cutting process; _Ww is the water energy consumed during the cutting process; _ηe is the electrical energy conversion efficiency; _ρw is the density of water; _cw is the specific heat capacity of water; ΔT is the temperature rise of water;

Cutting accuracy CP is expressed as:

Wherein, CP is the cutting accuracy, which refers to the similarity between the cut after cutting and the expected cut; ΔL is the deviation between the cut length after cutting and the expected length; ΔW is the deviation between the cut width after cutting and the expected width; _Ra is the surface roughness of the cut after cutting; D is the abrasive particle size;

Step S2: normalizing the experimental data and dividing them into a training set and a test set;

Step S3: constructing a radial basis function neural network model; the input layer of the radial basis function neural network model is the cutting process parameters, the output layer is the cutting process quality index, the activation function is the Gaussian function and the loss function is the mean square error;

Step S4: Optimizing the radial basis neural network model parameters using a genetic algorithm; the parameters include the number of hidden layer neurons, center vector, width, connection weight and bias, specifically including:

Initialize the parameters, set the population size to S, the maximum evolutionary generation to G _max , the initial crossover probability to P _c , the initial mutation probability to P _m , the number of elite individuals to E , the current generation to g = 0, the upper limit of the number of hidden layer neurons to M _max , the value range of the center vector and width parameter to [0, 1], and the value range of the connection weight and bias to [-1, 1];

Generate an initial population and randomly generate S individuals. Each individual consists of the number of hidden layer neurons M, the center vector C = [c ₁ , c ₂ , ..., c _M ], the width parameter ∑ = [σ ₁ , σ ₂ , ..., σ _M ], the connection weight W = [w ₁₁ , w ₁₂ , ..., w _M3 ] and the bias B = [b ₁ , b ₂ , b ₃ ], which can be expressed as:

X _s = [M, C, ∑, W, B], s = 1, 2,..., S

Where _Xs is the sth individual; M is an integer, satisfying _1≤M≤Mmax ; C, ∑, W and B are all real vectors, satisfying 0≤C, ∑≤1, -1≤W, B≤1;

Calculate the fitness. For each individual X _s , construct the RBF neural network according to its parameters, use the training set to calculate its loss function Loss _s , and then convert it into the fitness function F _s , expressed as:

In the formula, l is a very small positive number, which is used to avoid the situation where the denominator is zero;

Selection operation: Use the roulette method to select S individuals to enter the next generation, and retain E elite individuals, that is, the E individuals with the highest fitness, which do not participate in crossover and mutation operations and are directly copied to the next generation;

The crossover operation uses an adaptive crossover probability, expressed as:

Where, P _c,s is the crossover probability of the sth individual; g is the current generation; G _max is the maximum evolutionary generation;

For each pair of adjacent individuals, a crossover operation is performed according to their crossover probability, that is, some or all of the parameters are exchanged to generate two new individuals, including:

The number of hidden neurons M is crossed, a crossover point p is randomly selected, and then the first p bits of binary codes of M of the two individuals are exchanged to generate two new M values, which are expressed as:

M′ ₁ =M ₁ [1: p] + M ₂ [p + 1: M _max ]

M′ ₂ =M ₂ [1: p] + M ₁ [p + 1: M _max ]

Wherein, _M1 and _M2 are the original M values of the two individuals; _M′1 and _M′2 are the new M values of the two individuals; M[l:ζ] represents the binary code from the lth bit to the ζth bit of M; and 1≤p≤M _max -1 is satisfied;

The intersection of the center vector C randomly selects an intersection point a, and then exchanges the first a elements of C of the two individuals to generate two new C vectors, expressed as:

Wherein, C′ ₁ and C′ ₂ are the new C vectors of two individuals; c _sβ represents the βth central vector element of the sth individual; a satisfies 1≤a≤M _min ; M _min satisfies M _min =min(M′ ₁ ,M′ ₂ );

Crossover of width parameter ∑ randomly selects a crossover point r, and then exchanges the first r elements of ∑ of the two individuals to generate two new ∑ vectors, expressed as:

Where ∑′ ₁ and ∑′ ₂ are the new ∑ vectors of the two individuals; σ _sγ represents the γth central vector element of the sth individual; r satisfies 1≤r≤M _min ;

Connect the cross of weight W, randomly select a crossover point f, and then exchange the first f elements of W of the two individuals to generate two new W vectors, expressed as:

Where _W′1 and _W′2 are the new W vectors of the two individuals; _wsIJ is the connection weight from the Ith hidden layer neuron to the Jth output layer neuron of the sth individual; f satisfies _{1≤f≤3Mmin} ;

Biased crossover of B randomly selects a crossover point h, and then exchanges the first h elements of B of the two individuals to generate two new B vectors, expressed as:

B′ ₁ = [b ₁₁ , b ₁₂ ,…, b _1h , b _2h+1 , b _2h+2 ,…, b ₂₃ ]

B′ ₂ = [b ₂₁ , b ₂₂ ,…, b _2h , b _1h+1 , b _1h+2 ,…, b ₁₃ ]

Where B′ ₁ and B′ ₂ are the new B vectors of the two individuals; b _sJ is the bias of the Jth output layer neuron representing the sth individual; h satisfies 1≤h≤3;

The mutation operation uses adaptive mutation probability, expressed as:

Where, P _m,s is the mutation probability of the sth individual; g is the current generation; G _max is the maximum evolutionary generation;

For each individual, a mutation operation is performed according to its mutation probability, that is, a small perturbation is made to some or all of the parameters to generate a new individual, including:

The variation of the number of hidden layer neurons M randomly selects a crossover point o, and then flips the binary code of the oth bit to generate a new M value, which is expressed as:

M′＝M[1：o-1]+M[o]+M[o+1：M _max ]

Where M′ is the new value of M; M[o] represents the inverse of the binary code of the oth bit of M, that is, 0 becomes 1, and 1 becomes 0; 1≤o≤M _max is satisfied;

The mutation of the center vector C randomly selects an intersection point u, and then adds a random number that follows a normal distribution to the u-th element to generate a new C vector, which is expressed as:

C′=[c ₁ , c ₂ ,…, c _u +δ,…, c _M ,]

Where C′ is the new C vector; δ is a random number that obeys the normal distribution N(0,σ _c ); σ _c is a small standard deviation used to control the amplitude of variation; and 1≤u≤M′ is satisfied;

Variation of the width parameter ∑, randomly selecting a crossover point Then for the elements plus a random number that follows a normal distribution to generate a new ∑ vector, expressed as:

Where ∑′ is the new ∑ vector; δ is a random number that obeys the normal distribution N(0, σ _σ ); σ _σ is a small standard deviation used to control the amplitude of variation; satisfy

To mutate the connection weight W, randomly select a mutation point v, and then add a random number that follows a normal distribution to the vth element to generate a new W vector, which is expressed as:

W′=[w ₁₁ , w ₁₂ ,…, w _v +δ,…, w _3M′ ]

Where W′ is the new W vector; δ is a random number that obeys the normal distribution N(0,σ _w ), and σ _w is a small standard deviation used to control the amplitude of variation; satisfying 1≤v≤3M′;

The variation of bias B randomly selects a variation point z, and then adds a random number that follows a normal distribution to the zth element to generate a new B vector, which is expressed as:

B′=[b ₁ , b ₂ ,…, b _z + δ,…, b ₃ ]

Where B′ is the new B vector; δ is a random number that obeys the normal distribution N(0,σ _b ), and σ _b is a small standard deviation used to control the amplitude of variation; satisfying 1≤z≤3;

Termination condition: if the maximum number of evolutionary generations G _max is reached, or the fitness change of the population is less than the set threshold, the evolution is stopped, and the parameters and fitness of the optimal individual, as well as the corresponding radial basis neural network model, are output; otherwise, set g = g + 1, return to calculate the fitness, and continue the evolution;

Step S5: Use the test set to evaluate the prediction performance of the radial basis neural network model, calculate the error between the predicted value and the actual value; determine whether the error meets the error range, if it meets the error range, output the radial basis neural network model; if it does not meet the error range, retrain the radial basis neural network model.

2. The abrasive jet cold cutting quality prediction method according to claim 1, characterized in that the normalization of the experimental data specifically comprises:

Where N is the number of experimental data; X is the cutting process parameter matrix; Y is the cutting process quality index matrix;

Data normalization is expressed as:

In the formula, _xij and _yij are the cutting process parameters and cutting process quality indicators of the i-th sample respectively; xij _′ and _yij ′ are the cutting process parameters and cutting process quality indicators of the i-th sample after normalization respectively; _xj and _yj are the cutting process parameters and cutting process quality indicators of the j-th column respectively; min( _xj ) and max( _xj ) are the minimum and maximum values of the cutting process parameters of the j-th column respectively; min( _yj ) and max( _yj ) represent the minimum and maximum values of the cutting process quality indicators of the j-th column respectively.

3. The method for predicting the quality of abrasive jet cold cutting according to claim 1, wherein the step of constructing a radial basis function neural network model comprises:

The input layer of the radial basis neural network model is the cutting process parameters; the output layer is the cutting process quality index; the number of neurons in the hidden layer is M;

The activation function of the hidden layer is expressed as:

Where x is the data of the input layer, i.e., the normalized cutting process parameters; c _I is the center vector of the Ith hidden layer neuron; σ _I is the width parameter of the Ith hidden layer neuron; φ is the radial basis function, i.e., the Gaussian function; ||·|| is the Euclidean norm;

The output function of the output layer is expressed as:

Where y _J (x) is the output value of the J-th output layer neuron, that is, the normalized cutting quality index; w _IJ is the connection weight from the I-th hidden layer neuron to the J-th output layer neuron; b _J is the bias of the J-th output layer neuron;

The loss function is expressed as:

Where y _kJ is the actual value of the Jth cutting quality index of the kth sample; is the predicted value of the Jth cutting quality index of the kth sample; is the number of samples in the training set, that is, the number of partial experimental data.

4. An abrasive jet cold cutting quality prediction system, characterized in that the system comprises:

The experimental data collection module is used to collect cutting experimental data; the experimental data includes cutting process parameters and cutting processing quality indicators, specifically including:

The cross-sectional area A of the abrasive jet is expressed as:

The velocity V of the abrasive jet is expressed as:

Where, Q is the abrasive jet flow rate; V is the jet velocity;

The kinetic energy E _k of the jet is expressed as:

The pressure P of the jet is expressed as:

Where, P is the abrasive jet pressure;

The impact force F of the jet is expressed as:

The loss level LR is expressed as:

Wherein, LR is the loss degree; _ms is the mass of the sample after cutting; _ma is the mass of the abrasive consumed from the nozzle during the cutting process; _mn is the mass of the nozzle worn during the cutting process; _ρa is the abrasive density; _ρn is the nozzle density; t is the cutting time; ∈ is the nozzle wear coefficient; _m0 is the material mass before cutting, _m0 = _ms +m _a + _mn ;

Energy consumption EC is expressed as:

Cutting accuracy CP is expressed as:

A normalization processing and division module is used to normalize the experimental data and divide it into a training set and a test set;

A radial basis network construction module is used to construct a radial basis neural network model; the input layer of the radial basis neural network model is the cutting process parameter, the output layer is the cutting process quality index, the activation function is the Gaussian function and the loss function is the mean square error;

The network parameter optimization module is used to optimize the parameters of the radial basis neural network model using a genetic algorithm; the parameters include the number of hidden layer neurons, center vector, width, connection weight and bias, specifically including:

The parameter initialization submodule is used to initialize parameters, setting the population size to S, the maximum evolutionary generation to G _max , the initial crossover probability to P _c , the initial mutation probability to P _m , the number of elite individuals to E , the current generation to g = 0, the upper limit of the number of hidden layer neurons to M _max , the value range of the center vector and width parameter to [0, 1], and the value range of the connection weight and bias to [-1, 1];

The initial population generation submodule is used to generate the initial population and randomly generate S individuals. Each individual consists of the number of hidden layer neurons M, the center vector C = [c ₁ , c ₂ , ..., c _M ], the width parameter ∑ = [σ ₁ , σ ₂ , ..., σ _M ], the connection weight W = [w ₁₁ , w ₁₂ , ..., w _M3 ] and the bias B = [b ₁ , b ₂ , b ₃ ], which can be expressed as:

X _s = [M, C, ∑, W, B], s = 1, 2,..., S

The fitness calculation submodule is used to calculate the fitness. For each individual X _s , an RBF neural network is constructed according to its parameters, and its loss function Loss _s is calculated using the training set, and then converted into a fitness function F _s , which is expressed as:

The selection submodule is used to perform selection operations. It uses the roulette method to select S individuals to enter the next generation, while retaining E elite individuals, that is, the E individuals with the highest fitness, which do not participate in crossover and mutation operations and are directly copied to the next generation;

The crossover submodule is used to perform a crossover operation using an adaptive crossover probability, expressed as:

M′ ₁ =M ₁ [1: p] + M ₂ [p + 1: M _max ]

M′ ₂ =M ₂ [1: p] + M ₁ [p + 1: M _max ]

Where _B′1 and _B′2 are the new B vectors of the two individuals; _bsJ is the bias of the Jth output layer neuron representing the sth individual; h satisfies 1≤h≤3;

The mutation submodule is used to perform mutation operations and uses an adaptive mutation probability, expressed as:

M′＝M[1：o-1]+M[o]+M[o+1：M _max ]

C′=[c ₁ , c ₂ ,…, c _u + δ,…, c _M′ ]

W′=[w ₁₁ , w ₁₂ ,…, w _v +δ,…, w _3M′ ]

B′=[b ₁ , b ₂ ,…, b _z + δ,…, b ₃ ]

The conditional termination submodule is used for termination conditions. If the maximum number of evolutionary generations G _max is reached, or the fitness change of the population is less than the set threshold, the evolution is stopped and the parameters and fitness of the optimal individual, as well as the corresponding radial basis neural network model, are output; otherwise, g=g+1 is set, the calculated fitness is returned, and the evolution continues;

The model performance evaluation module is used to evaluate the prediction performance of the radial basis neural network model using a test set, calculate the error between the predicted value and the actual value; determine whether the error meets the error range, if it meets the error range, output the radial basis neural network model; if it does not meet the error range, retrain the radial basis neural network model.

5. The abrasive jet cold cutting quality prediction system according to claim 4, characterized in that the normalization processing division module specifically comprises:

Data normalization is expressed as:

6. The abrasive jet cold cutting quality prediction system according to claim 4, characterized in that the radial basis network construction module specifically comprises:

The activation function of the hidden layer is expressed as:

The output function of the output layer is expressed as:

The loss function is expressed as: