Multi-output regression prediction method for small samples in laser processing process

Abstract

Disclosed is a multi-output regression prediction method for small samples in a laser processing process, which relates to the technical field of machine learning, and uses an adaptive dynamic genetic algorithm (ADGA) and an adaptive moment estimation algorithm (AM) to jointly optimize an artificial neural network (ANN), the algorithms being based on enhanced small samples. Data enhancement is achieved by adding noise to output data in the laser processing process, the ADGA is used to search for optimal parameters of the ANN on a global scale, and the AM is used to optimize the gradients of the optimal parameters, thereby accelerating the convergence speed of the model and enhancing the external prediction stability of the model. When the sample size in laser processing is insufficient, stable and accurate small-sample multi-output prediction can be carried out, thereby improving processing efficiency and reducing production costs in laser processing.

Description

A multi-output regression prediction method for small samples in laser machining process Technical Field

[0001] The present invention relates to the field of machine learning technology, and more particularly to a multi-output regression prediction method for small samples in a laser processing process. Background Art

[0002] During laser processing, many factors influence the quality of the process, requiring precise setting of process parameters. Predicting these parameters is a multi-objective optimization problem. If a sufficient number of samples satisfy the data distribution characteristics and accuracy, a neural network with high prediction accuracy can be trained. However, in actual laser processing cases, it is difficult to obtain sufficient labeled data. Insufficient sample size or suboptimal data distribution can result in the neural network being unable to learn the distribution of the data in the region, reducing the prediction accuracy of the neural network model. The characteristics of small sample datasets are often the focus of research, and extracting valid information from them is difficult. Therefore, multi-output regression prediction (MORP) based on small samples requires further research.

[0003] Currently, some exploration has been conducted on MORP for small samples in laser processing, but the research mainly focuses on small sample enhancement for single-output neural networks, insufficient sample size for training small samples, and difficulty in training small samples. In MORP, insufficient samples often lead to low precision and poor stability of the established model. Low precision leads to inaccurate multi-output prediction results, thereby reducing processing efficiency, and poor stability increases experimental costs. Insufficient sample size may lead to overfitting, so enhancement methods are needed to expand the sample size. However, changes in the original sample will generate noise, affecting the accuracy and stability of the prediction, and ANN-based predictions will also show instability. At the same time, due to the strong interrelationships between the various parameters in laser processing, single-input and output ANN predictions cannot meet the requirements for precise setting of process parameters.

[0004] Therefore, how to improve the accuracy and stability of multi-output regression prediction when the sample capacity is insufficient is a problem that those skilled in the art need to solve urgently.

[0005] Summary of the Invention

[0006] In view of this, the present invention provides a multi-output regression prediction method for small samples in the laser processing process. It is a general, low-complexity, easy-to-implement new MORP method based on small samples in industrial laser processing. By constructing ADGA to optimize the internal structure parameters of the neural network and using AM to optimize the gradient, this method takes into account the accuracy of multiple prediction variables, balances the stability of internal and external predictions, and solves the problem of relatively high computational cost.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] A multi-output regression prediction method for small samples in laser processing includes the following steps:

[0009] Step 1: Collect sample data and preprocess it to obtain output data, add noise samples to the output data, and construct the hyperparameters of the artificial neural network ANN;

[0010] In the process of model prediction, small samples are prone to overfitting, so the data must be enhanced and noise samples must be added to the output data, expressed as: Y o (X1,···,X n )=[Y1(X1,···,X n ) T ,Y2(X1,···,X n ) T ,Y m (X1,···,X n ) T ],

[0011] Where X1,…,X n are n factors that affect a certain performance of laser processing, i.e., input variables; Y1(X1,…,X n ),Y2(X1,…,X n ),…,Y m (X1,…,X n ) represents the m laser processing performance evaluation indicators (output variables) predicted by the proposed model when n influencing factors (input variables) are considered; Y o (X1,…,X n ) represents the output data of the prediction model; is the output after adding noise, that is, the hyperparameter; T represents the transpose; λ is the noise intensity; ψ(u,v) is the matrix generated by the standard positive distribution; u is the dimension of the output; v is the number of training set samples in the sample data;

[0012] Step 2: Search for the optimal weights and thresholds based on the adaptive dynamic genetic algorithm (ADGA) and input them into the ANN;

[0013] Based on the traditional genetic algorithm, the random crossover and mutation are improved to obtain the ADGA optimization method, which makes it adaptive and dynamic. The steps of the ADGA optimization method to search for the optimal weights and thresholds in the ANN weights and thresholds are as follows:

[0014] Step 21: Use real number coding to encode the initial population separately. The coded individuals corresponding to the initial population are called chromosomes in the genetic algorithm, and their genes constitute the weight set and threshold set of the ANN;

[0015] Step 22: Calculate the fitness of each chromosome; the fitness function for calculating the fitness uses the mean square error function of the test set, which is expressed as:

[0016] Among them, n ts is the number of test set samples in the sample data; n o is the number of neurons in the output layer; and Y t l (k) are the output data (actual output value) and expected output value of the lth output variable in the test set; fit represents the fitness of each chromosome in the population; that is, the mean square error is obtained by comparing the predicted value obtained by the ANN training model with the actual value obtained in the experiment; the expected output value is obtained through the laser processing experiment;

[0017] Step 23: When the i-th chromosome is generated, the fitness of the i-th chromosome is compared with the fitness of each chromosome in the population composed of the previous chromosomes to obtain the minimum fitness value fit min (i), as the minimum fitness value fit of the current population min By comparing the fitness, the chromosome corresponding to the minimum fitness value is taken as the best chromosome CS bs ;

[0018] Step 24: Calculate the adaptive dynamic crossover probability p c and adaptive dynamic mutation probability p m , respectively calculated as:

[0019] Among them, p cmax and p cmin are the maximum and minimum crossover probabilities respectively; p mmax and p mmin are the maximum and minimum values ​​of the mutation probability respectively; n t and N t Represent the current evolutionary generation and the maximum evolutionary generation respectively; From the above equations, it can be seen that crossover and mutation operations are performed within a certain range and will change with the changes in genetic generations and fitness values, so they are adaptive and dynamic;

[0020] Step 25: Calculate the probability of each chromosome being selected;

[0021] Perform a selection operation and use the roulette wheel to select excellent genes. Therefore, the fitness value is proportional to the probability of individual selection. The maximum cumulative probability is selected as the selection probability. An error function is selected as the fitness function, and its inverse is used to define the probability p of selecting the jth chromosome. j , expressed as:

[0022] Among them, κ is a constant adjustment factor, which is taken as 10; fit j is the fitness of the jth chromosome; the population size is p s If the selection probability is greater than the adaptive dynamic crossover probability p c and adaptive dynamic mutation probability p m , then go to step 26, otherwise do not perform the adaptive dynamic crossover operation and the adaptive dynamic mutation operation, and go to step 28;

[0023] Step 26: Perform adaptive dynamic crossover operation using real number crossover method according to the code corresponding to each chromosome to obtain the best chromosome;

[0024] Corresponding to the real number encoding of chromosomes, the adaptive dynamic crossover operation uses real number crossover, the purpose of which is to breed new chromosomes with good genes from their parents; the crossover equation is:

[0025] in, is the kth gene of the i-th chromosome; is the k-th gene of the j-th chromosome, and r is a random number in [0,1];

[0026] Step 27: Adaptive dynamic mutation is used to generate new excellent chromosomes, expressed as:

[0027] Among them, CS i r is the rth gene of the i-th chromosome; CS max and CS min are the upper and lower bounds respectively; σ is a random number in [0,1]; at the same time, f(n t )=ζ(1-n t / N t ) 2

[0028] Where ζ is a random number in [0,1];

[0029] The optimal chromosome is input into the initial optimal weights and thresholds of the ANN training model, which are then used to optimize their gradients and update them. This helps to improve the convergence speed of the training model and deepen the stability of its prediction results each time, so as to obtain the optimal prediction model with the least amount of calculation;

[0030] Step 28: Update the population, calculate the fitness of the new population according to the fitness function in step 22, and obtain the fitness of each chromosome;

[0031] Fit the current chromosome fitness of the new population cur Updated to The minimum fitness of the new population is fit min Updated to Select the chromosome corresponding to the minimum fitness and finally get a new optimal chromosome

[0032] By comparing the best chromosome CS in step 23 bs and optimal chromosomes The fitness of the chromosome with the smallest fitness is selected as the final search chromosome, and the iterative evolution process is carried out until the maximum evolutionary generation is reached. The ADGA optimization process is terminated, and the final search chromosome at the termination corresponds to the optimal weight and threshold;

[0033] Step 29: Repeat steps 24 to 28 until the maximum number of evolution generations is reached.

[0034] Step 3: Optimize the gradient of the optimal weight and the optimal threshold according to the adaptive moment estimation algorithm (AM), train the ANN, and obtain the optimal training model; the specific steps are:

[0035] Step 31: Determine the weight gradient and threshold gradient according to the objective function of ANN,

[0036] To optimize ANN using the AM algorithm, it is necessary to determine the objective function, that is, the mean square error function E of the training set. T ; According to the error function, and They represent the gradients of the connection weights from the hidden layer to the output layer, from the input layer to the hidden layer, and the gradients of the thresholds of the output layer and the hidden layer. and These calculations are as follows

[0037] in, represents partial derivative;

[0038] Step 32: Use the determined weight gradient and threshold gradient as the gradient stochastic objective function, and solve the first-order and second-order partial estimates of the weight and threshold;

[0039] The gradient of the connection weights from the hidden layer to the output layer and from the input layer to the hidden layer and As a gradient stochastic objective function and Similarly, the gradient of the threshold of the output layer and the hidden layer and As a gradient stochastic objective function and That is, the first-order and second-order partial estimates, m t and v t Updated to

[0040] in, and They are the updated connection weights from the hidden layer to the output layer and the unupdated partial first-order moment estimates; and They are the updated connection weights from the input layer to the hidden layer and the unupdated partial first-order moment estimates; and denote the updated and unupdated partial first-order moment estimates of the output layer threshold, and the updated and unupdated partial first-order moment estimates of the hidden layer threshold, respectively; and They are the update of the connection weights from the hidden layer to the output layer and the unupdated partial second-order raw moment estimate, as well as the update of the connection weights from the input layer to the hidden layer and the unupdated partial second-order raw moment estimate; and are the updated and unupdated partial second-order raw moment estimates of the output layer threshold, and the updated and unupdated partial second-order raw moment estimates of the hidden layer threshold; the exponential decay rates of the moment estimates are denoted as β1 and β2, respectively, and their values ​​are taken in the interval [0,1);

[0041] Step 33: bias correction is performed on the first-order and second-order bias estimates to obtain bias-corrected first-order moment estimates and bias-corrected second-order moment estimates of weights and thresholds; the bias-corrected first-order and second-order moment estimates are calculated as follows:

[0042] in, and are the bias-corrected first-order moment estimates of the connection weights from the hidden layer to the output layer and from the input layer to the hidden layer, respectively; and are the bias-corrected first-order moment estimates of the output layer and hidden layer thresholds, respectively; and are the bias-corrected second-order raw moment estimates of the connection weights from the hidden layer to the output layer and from the input layer to the hidden layer, respectively; and are the bias corrections performed on the second-order raw moment estimates of the output layer and the hidden layer respectively; it represents the current iteration number of the ANN;

[0043] Step 34: Calculate the optimal weights and thresholds based on the bias-corrected first-order moment estimates and bias-corrected second-order moment estimates of the weights and thresholds;

[0044] Update the corresponding weights and thresholds to obtain the optimal weights and thresholds, the expressions are:

[0045] in, and W ho are the updated and non-updated connection weights from the hidden layer to the output layer, respectively; and W ih are the updated and non-updated connection weights from the input layer to the hidden layer, respectively; and B o are the updated and unupdated thresholds of the output layer respectively; similarly, and B h are the updated threshold and the unupdated threshold from the hidden layer respectively; α is the step size; and to prevent singularity, ε is always positive;

[0046] Step 35: Repeat the above process from step 31 to step 34 until the current number of iterations reaches the set maximum number of iterations or the mean square error calculated by the mean square error function of the training set reaches the set minimum error level. The ANN training is then completed. The initial optimal weights and threshold gradients obtained by ADGA optimization are used to continuously train the training model with the best prediction effect. At this time, the training model can more accurately predict the corresponding multiple evaluation indicators based on the multiple influencing factors input.

[0047] Through the above technical solutions, it can be seen that compared with the existing technology, the present invention discloses a multi-output regression prediction method for small samples in the laser processing process. This method requires predicting multiple features of small samples. This method has certain reliability and practicality for industrial laser processing tools based on multi-output regression prediction (MORP) of small samples. By adding noise to the output data to enhance the sample, overfitting caused by insufficient sample capacity is avoided. The added noise will interfere with the prediction results, thereby affecting the prediction accuracy of the model and causing fluctuations in the prediction process. In order to improve the accuracy and improve the stability of internal prediction, the method uses an adaptive genetic algorithm to improve the crossover and mutation of the fixed probability population in the traditional genetic algorithm to adaptive dynamic crossover and adaptive dynamic mutation. This is caused by the change of evolutionary generations and fitness values ​​within a certain probability range. In order to accelerate the convergence speed of the ANN and enhance the external prediction stability of the model, AM is used to optimize the gradients of the weights and thresholds. Therefore, this method is effective and feasible, improves the global search capability and search stability of the genetic algorithm, and improves the convergence speed of the ANN. Compared with other methods, this method not only achieves multi-input and output prediction with a moderate amount of computation, but also greatly improves the prediction accuracy and the stability of internal and external predictions. This prediction stability provides a solid foundation for making correct decisions. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0049] FIG1 is a schematic diagram of the ADGA+AM+ANN prediction model provided by the present invention;

[0050] FIG2 is a schematic diagram of the basic structure of the back propagation neural network provided by the present invention. DETAILED DESCRIPTION

[0051] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0052] The embodiment of the present invention discloses a multi-output regression prediction method for small samples in laser processing, which adopts an ADGA+AM+ANN structure prediction model, as shown in FIG1 . The specific steps are as follows:

[0053] S1: Add noise samples to the preprocessed output data to construct the hyperparameters of the ANN; in the model prediction process, small samples are prone to overfitting, so the data must be enhanced and noise must be added to the output data.

[0054] Where X1, X2, and X3 are the three factors affecting laser cladding: laser power P (W), scanning speed v (mm / s), and shielding gas volume G (L / min), i.e., three input variables; Y1 (X1, X2, X3), Y2 (X1, X2, X3), and Y3 (X1, X2, X3) mean that when the above three variables are input, the three indicators for evaluating the performance of the cladding layer predicted by the proposed model at the same time are: cladding layer height H (μm), cladding layer width W (μm), and hardness Ha (HV 0.5 ) are three output variables; Y o (X1,…,X n ) is the output; is the output after adding noise; T represents transpose; λ is the noise intensity; ψ(u,v) is the matrix generated by the standard positive distribution; u is the dimension of the output; v is the number of samples;

[0055] S2: Build an ANN-based ANN training model based on hyperparameters;

[0056] Backpropagation neural networks are the most mature and widely used type of ANN. They are usually determined by a single input and output layer, separated by a hidden layer, which can be composed of one or more layers. A single hidden layer must be used when the function involves a continuous mapping from one finite space to another finite space. The number of independent and dependent variables is the number of neurons in the input and output layers respectively. The number of hidden layer neurons is usually determined as follows,

[0057] Among them, n h , n i , n o and n s are the number of neurons and samples in the hidden layer, input layer, and output layer respectively; c is a constant between 1 and 10; C is a probability combination; i is [0, n i ] integers in the range;

[0058] An activation function is required between layers, usually a sigmoid function; in MOP, the equation is

[0059] in are the linear combinations of n-dimensional samples and their corresponding weights W and thresholds B;

[0060] Backpropagation neural networks typically include forward propagation of signals and backpropagation of errors; forward propagation is activated by initial random weights and thresholds, followed by backpropagation; the expected value is compared with the actual value to obtain the total mean square error, which is expressed as:

[0061] Among them, E T represents the error function, and Y t j (k) are the actual output value and expected output value of the j-th dependent variable in the test set, and the number of samples in the test set is n tr ;

[0062] The error signal is transmitted to the hidden layer; the connection weights and thresholds between the output layer and the hidden layer are corrected, and the error signal is transmitted from the hidden layer to the input layer; the connection weights and thresholds between the hidden layer and the input layer are modified;

[0063] Repeat the back-and-forth training until the error reaches the minimum or the training frequency reaches the maximum, as shown in Figure 2;

[0064] S3: The ADGA optimization method and the AM algorithm are used to jointly optimize the ANN training model to obtain a multi-output prediction (MOP) model;

[0065] S31: Search for optimal weights and thresholds according to the ADGA optimization method and input them into the ANN training model;

[0066] The ADGA optimization method is based on the traditional genetic algorithm, which improves random crossover and mutation to make it adaptive and dynamic. The specific process is as follows:

[0067] The initial population is individually encoded using real number coding. The individuals in the encoded initial population are called chromosomes in the genetic algorithm, and their genes constitute the weight set and threshold set of the ANN;

[0068] Calculate the fitness of each chromosome; individuals with high fitness will be retained to form a new population; the fitness function is expressed as the error function of the test set,

[0069] Among them, n ts is the number of test set samples, and Y t l(k) are the actual output value and expected output value of the lth dependent variable in the test set, and then the fitness fit of each chromosome in the population is obtained;

[0070] When the i-th chromosome is generated, the minimum fitness value of the population composed of the i-th chromosome and its previous population is expressed as fit min (i) Get the minimum fitness value fit of the current population min , get the best chromosome CS by comparing fitness bs ;

[0071] Adaptive dynamic crossover probability p c and adaptive dynamic mutation probability p m Calculated as:

[0072] Among them, p cmax and p cmin are the maximum and minimum crossover probabilities respectively; p mmax and p mmin are the maximum and minimum values ​​of the mutation probability respectively; n t and N t Represent the current and maximum evolutionary generations respectively; From the above equations, it can be seen that crossover and mutation operations are performed within a certain range and will change with the changes in genetic generations and fitness values, so they are adaptive and dynamic;

[0073] Perform a selection operation and use the roulette wheel to select excellent genes, so the fitness value is proportional to the probability of individual selection; select an error function as the fitness function, and use its inverse to define the probability of selecting the jth chromosome,

[0074] Among them, κ is a constant adjustment factor, which is taken as 10; fit j is the fitness value of the jth chromosome; the population size is p s ;

[0075] An adaptive dynamic crossover operation is performed; corresponding to the real number encoding of chromosomes, the adaptive dynamic crossover operation uses real number crossover, the purpose of which is to breed new chromosomes with good genes of their parents; the crossover equation is

[0076] in, is the kth gene of the i-th chromosome; is the k-th gene of the j-th chromosome, and r is a random number in [0,1];

[0077] Adaptive dynamic mutation is used to generate new excellent chromosomes.

[0078] Among them, CS i r is the rth gene of the i-th chromosome; CS max and CS min There are upper and lower bounds respectively; σ is a random number in [0,1]; at the same time, f(n t )=ζ(1-n t / N t ) 2 (13);

[0079] Where ζ is a random number in [0,1];

[0080] After the iterative evolution process, the population is updated, and the fitness of the new population is calculated according to formula (6) to obtain the fitness value of each chromosome; the current chromosome fitness of the new population is fit cur Updated to Fit the minimum fitness of the current population min Updated to

[0081] Select the chromosome corresponding to the minimum fitness and finally get a new optimal chromosome By comparing CS bs and The fitness of the chromosome is obtained by selecting the smallest one and performing the iterative evolution process until the maximum evolutionary generation is reached. The optimization process of the ADGA optimization algorithm is terminated.

[0082] S32: Optimize the gradient of the optimal weight and threshold according to the AM algorithm, train the ANN, obtain the optimal training model, and obtain the MORP model;

[0083] To optimize ANN using AM, it is necessary to determine the objective function, namely the mean square error function E T ;

[0084] Then get and They represent the gradient of the connection weights from the hidden layer to the output layer, from the input layer to the hidden layer, and the threshold from the output layer to the hidden layer. and The gradients of ; these are calculated as follows:

[0085] in, Represents partial derivatives; obtain the gradient random function of the connection weights from the hidden layer to the output layer and from the input layer to the hidden layer respectively and Right now and same, and are the gradient stochastic objective functions of the thresholds of the output layer and the hidden layer, that is, and

[0086] First-order and second-order partial estimates, m t and v t Updated to

[0087] in, and They are the updated connection weights from the hidden layer to the output layer and the unupdated partial first-order moment estimates; and They are the updated connection weights from the input layer to the hidden layer and the unupdated partial first-order moment estimates; and denote the updated and unupdated partial first-order moment estimates of the output layer and hidden layer thresholds, respectively; and They are the updated and unupdated partial second-order raw moment estimates of the connection weights from the hidden layer to the output layer and the updated and unupdated partial second-order raw moment estimates of the connection weights from the input layer to the hidden layer; and are the updated and unupdated partial second-order raw moment estimates of the output layer threshold, and the updated and unupdated partial second-order raw moment estimates of the hidden layer threshold; the exponential decay rates of the moment estimates are denoted as β1 and β2, respectively, and their values ​​are taken in the interval [0,1);

[0088] The bias-corrected first-order and second-order moment estimates are calculated as

[0089] in, and are the bias-corrected first-order moment estimates of the connection weights from the hidden layer to the output layer and from the input layer to the hidden layer, respectively; and are the bias-corrected first-order moment estimates of the output layer and hidden layer thresholds, respectively; and are the bias-corrected second-order raw moment estimates of the connection weights from the hidden layer to the output layer and from the input layer to the hidden layer, respectively; and are the bias corrections performed on the second-order raw moment estimates of the output layer and the hidden layer respectively; it represents the current iteration number of the ANN;

[0090] Finally, the corresponding weights and thresholds are updated as

[0091] in, and W ho are the updated and non-updated connection weights from the hidden layer to the output layer, respectively; and W ih are the updated and non-updated connection weights from the input layer to the hidden layer, respectively; and B o are the updated and unupdated thresholds of the output layer respectively; similarly, and B h are from the hidden layer and the updated threshold and the unupdated threshold respectively; α is the step size; at the same time, in order to prevent singularity, ε is always positive; repeat the above process until the error reaches the minimum value or the training frequency reaches the maximum value, and the ANN training is completed. At this time, the training model can more accurately predict the corresponding multiple evaluation indicators based on multiple influencing factors of the input.

[0092] Example

[0093] The effectiveness and feasibility of ADGA-AM-ANN are verified using laser cutting data. The experimental data in "Multi-response optimization of laser cladding for TiC particle reinforced Fe matrix composite based on Taguchi method and grey relational analysis" (10.1016 / J.OPTLASTEC.2022.108259) are cited, and the laser power P (W), scanning speed v (mm / s), and shielding gas volume G (L / min) are taken as the three factors affecting laser cladding, as shown in the second to fourth columns of Table 1, as the input learning parameters of the prediction model; the cladding layer height H (μm), cladding layer width W (μm), and hardness Ha (HV 0.5) is used as the evaluation index of the cladding layer performance, as shown in the 5th to 7th columns of Table 1, and is used as the output learning parameter of the prediction model.

[0094] Table 1: Laser processing experimental data

[0095] After the prediction model learns the above 25 groups of data, the output parameters (coating height, coating width, hardness) of the prediction models of groups 16 to 25 are taken out and compared with the actual experimental data and the relative error analysis is performed, as shown in Table 2:

[0096] Table 2: Comparison of model predictions and actual experimental values

[0097] The accuracy of the prediction method proposed in this paper is readily apparent from the data comparison and error analysis in the table above. The method's parameter selection is adaptive and dynamic, adjusting as the prediction results change, continuously approaching the optimal selection. This method exhibits the most reliable generalization and robustness. Its accuracy enables rapid identification of key influencing factors in the laser machining process, facilitating experimental progress. Its reliable stability significantly reduces the cost of laser machining and provides advantages for small-sample, multi-output prediction. The method is also relatively time-efficient.

[0098] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0099] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A multi-output regression prediction method for small samples in laser processing, characterized by: The specific steps include: Step 1: Collect parameter data during the laser processing process as sample data, perform preprocessing, add noise samples to the output data of the preprocessed sample data, and construct hyperparameters; Step 2: constructing an ANN-based prediction model according to the hyperparameters, using an adaptive dynamic genetic algorithm to search for optimal weights and optimal thresholds, and inputting them into the prediction model; Step 3: Adopting an adaptive moment estimation algorithm to optimize the gradient of the optimal weight and the optimal threshold, and training the prediction model to obtain a multi-output regression prediction model; Step 4: Collect the data to be predicted, input it into the multi-output regression prediction model, and obtain the prediction results.

2. The multi-output regression prediction method for small samples in laser processing according to claim 1, characterized in that: The specific implementation process of step 1 is: after pre-processing the sample data, add the noise sample to the output data, the expression is: Y o (X1,···,X n )=[Y1(X1,···,X n ) T ,Y2(X1,···,X n ) T ,Y m (X1,···,X n ) T ], Among them, X1,…,X n are n factors that affect the laser processing performance, which serve as the input variables of the prediction model; Y1(X1,…,X n ),Y2(X1,…,X n ),…,Y m (X1,…,X n ) represents the m evaluation indicators predicted by the prediction model simultaneously when n influencing factors are considered, as the output variables of the prediction model; Y o (X1,…,X n ) represents the output data of the prediction model; is the output data after adding noise, which serves as a hyperparameter; T represents transpose; λ is the noise intensity; ψ(u,v) is a matrix generated by the standard positive distribution; u is the dimension of the output data; v is the number of training set samples in the sample data.

3. The multi-output regression prediction method for small samples in laser processing according to claim 1, characterized in that: The random crossover and mutation in the genetic algorithm are improved into adaptive dynamic crossover and adaptive dynamic mutation to obtain the adaptive dynamic genetic algorithm, and the adaptive dynamic genetic algorithm is used to optimize the weight set and threshold set in the prediction model to obtain the optimal weight and the optimal threshold.

4. The multi-output regression prediction method for small samples in laser processing according to claim 3, characterized in that: The specific steps of using the adaptive dynamic genetic algorithm for optimization are: Step 21: using real number coding to individually encode the chromosomes in the initial population, the genes of the chromosomes constitute the weight set and threshold set of the prediction model; Step 22: Use the error function of the test set in the sample data as the fitness function to calculate the fitness of each chromosome, expressed as: Among them, n ts is the number of test set samples in the sample data; n o is the number of neurons in the output layer; and are the output data and expected output value of the lth output variable in the test set respectively; fit represents the fitness of each chromosome in the population; Step 23: The chromosomes whose fitness is higher than the set threshold form a new population. When the new population generates the i-th chromosome, the minimum fitness of the population composed of the i-th chromosome and the previous chromosomes is fit min (i), as the minimum fitness of the current population fit min , the chromosome corresponding to the minimum fitness is taken as the best chromosome CS bs ; Step 24: Calculate the adaptive dynamic crossover probability p c and adaptive dynamic mutation probability p m , expressed as: Among them, p cmax and p cmin are the maximum crossover probability and the minimum crossover probability respectively; p mmax and p mmin are the maximum mutation probability and the minimum mutation probability respectively; n t and N t Represent the current evolutionary generation and the maximum evolutionary generation respectively; Step 25: Calculate the selection probability of each chromosome according to the inverse of the fitness function, and perform a selection operation according to the selection probability. If the selection probability is greater than the adaptive dynamic crossover probability p c and adaptive dynamic mutation probability p m , then go to step 26, otherwise do not perform the adaptive dynamic crossover operation and the adaptive dynamic mutation operation, and go to step 28; the expression for calculating the selection probability is: Where κ is a constant regulatory factor; fit j is the fitness of the jth chromosome; p s is the population size; Step 26: Use the code corresponding to the selected chromosome to perform an adaptive dynamic crossover operation to breed a new chromosome with the optimal gene; the expression of the adaptive dynamic crossover operation is: in, is the kth gene of the i-th chromosome; is the k-th gene of the j-th chromosome, and r is a random number in [0,1]; Step 27: Adaptive dynamic mutation is used to generate a new optimal chromosome, which is expressed as: f(n t )=ζ(1-n t / N t ) 2 in, is the rth gene of the i-th chromosome; CS max and CS min are the upper and lower bounds respectively; σ is a random number in [0,1]; ζ is a random number in [0,1]; Step 28: Update the population and use the fitness function to calculate the fitness of each chromosome in the new population. Update the chromosome corresponding to the minimum fitness in the new population to the new best chromosome Select the best chromosome CS in step 23 bs and the new best chromosome The chromosome with the smallest fitness is selected as the final search chromosome, and the genes of the final search chromosome correspond to the optimal weights and thresholds; Step 29: Repeat steps 24 to 28 until the maximum number of evolution generations is reached.

5. The MORP method for small samples in laser processing according to claim 1, characterized in that: The prediction model includes an input layer, a hidden layer, and an output layer; the adaptive moment estimation algorithm is used to optimize the gradient of the optimal weight and the optimal threshold in the prediction model, and the prediction model is trained to obtain the multi-output regression prediction model. The specific implementation process is as follows: Step 31: Determine the weight gradient and threshold gradient according to the objective function of the prediction model, and the expression is: in, and Respectively represent the weight gradients from the hidden layer to the output layer and from the input layer to the hidden layer; and Respectively represent the threshold gradients of the output layer and the hidden layer; E T represents the objective function; represents partial derivative; Step 32: Using the weight gradient and the threshold gradient as the gradient random objective function, calculate the first-order partial estimate and the second-order partial estimate of the weight and the threshold, and obtain the weight updated partial first-order moment estimate, the weight not updated partial first-order moment estimate, the threshold updated partial first-order moment estimate, the threshold not updated partial first-order moment estimate, Weight updated partial second-order raw moment estimation, weight not updated partial second-order raw moment estimation, threshold updated partial second-order raw moment estimation, threshold not updated partial second-order raw moment estimation; the expression is: in, and They represent the weight gradient stochastic objective functions from the hidden layer to the output layer and from the input layer to the hidden layer respectively; and denote the threshold gradient stochastic objective functions of the output layer and the hidden layer respectively; and They are the updated partial first-order moment estimation of the weights from the hidden layer to the output layer and the unupdated partial first-order moment estimation of the weights; and They are the updated partial first-order moment estimation of the weight from the input layer to the hidden layer and the unupdated partial first-order moment estimation of the weight; and They represent the output layer threshold updated partial first-order moment estimate and the threshold not updated partial first-order moment estimate, as well as the hidden layer threshold updated partial first-order moment estimate and the threshold not updated partial first-order moment estimate; and They are respectively the updated partial second-order raw moment estimation of the weight from the hidden layer to the output layer and the unupdated partial second-order raw moment estimation of the weight, and the updated partial second-order raw moment estimation of the weight from the input layer to the hidden layer and the unupdated partial second-order raw moment estimation of the weight; and are the output layer threshold updated partial second-order raw moment estimate and the threshold not updated partial second-order raw moment estimate, and the hidden layer threshold updated partial second-order raw moment estimate and the threshold not updated partial second-order raw moment estimate; β1 and β2 represent the exponential decay rates of the moment estimates, respectively; Step 33: Perform bias correction on the biased first-order moment estimate and biased second-order raw moment estimate of the weight and threshold to obtain the weight bias-corrected first-order moment estimate, the threshold bias-corrected first-order moment estimate, the weight bias-corrected second-order raw moment estimate, and the threshold bias-corrected second-order raw moment estimate, which are expressed as follows: in, and They are the first-order moment estimation of weight deviation correction from hidden layer to output layer and the first-order moment estimation of weight deviation correction from input layer to hidden layer respectively; and They are the threshold bias-corrected first-order moment estimation of the output layer and the threshold bias-corrected first-order moment estimation of the hidden layer; and They are the second-order original moment estimation of weight deviation correction from hidden layer to output layer and the second-order original moment estimation of weight deviation correction from input layer to hidden layer; and They are the threshold bias-corrected second-order original moment estimation of the output layer and the threshold bias-corrected second-order original moment estimation of the hidden layer; it represents the current number of iterations; Step 34: Update the optimal weight and optimal threshold according to the weight deviation corrected first-order moment estimate, the threshold deviation corrected first-order moment estimate, the weight deviation corrected second-order original moment estimate, and the threshold deviation corrected second-order original moment estimate. The expression is: in, and W ho are the updated and non-updated weights from the hidden layer to the output layer respectively; and W ih are the updated weights and non-updated weights from the input layer to the hidden layer respectively; and B o are the updated threshold and non-updated threshold of the output layer respectively; and B h are the updated threshold and the unupdated threshold of the hidden layer respectively; α is the step size; ε is a set positive constant; Step 35: Loop the steps 31 to 34 until the current number of iterations reaches the maximum number of iterations or the objective function E T The calculated mean square error reaches the set minimum error level, and the latest updated weights and updated thresholds are substituted into the prediction model to obtain the multi-output regression prediction model.

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