The Prediction of Laser-Arc Hybrid Welding Bead Shape Basing On Multiple Population Genetic Algorithm and Neural Networks

Abstract

Abstract  In hybrid welding, due to the large number of welding parameters and the coupling between different welding parameters, any change of welding parameters will have a significant impact on the weld section size, so it is always essential to choose reasonable welding parameters to improve the stability of the weld. In this paper, an automatic measurement system for weld section size is designed. The center point of the weld section contour is taken as the origin of the polar coordinate system, and the pixel coordinates of the boundary points on the weld section contour are detected every 15 degrees. Based on 32 groups of laser-arc hybrid welding experiments, the BP (Back Propagation) neural network is used to establish the prediction model between the input parameters (welding current, laser power, welding Angle, welding gap, and weld blunt) and the output weld section size. Aiming to the problem of too many input and output parameters of the BP neural network, a multiple population genetic algorithm (MPGA) is introduced to optimize the internal weights and thresholds of the BP neural network to improve the prediction accuracy. Finally, the difference between the dimensions of the left and right sides of the weld is calculated as the symmetry of the weld profile. The results show that the measurement accuracy of the automatic measurement system can reach 98%, and the prediction accuracy of the section size and symmetry can reach about 90% with the optimized BP neural network. The research method in this paper is of great significance to the study of welding process parameter optimization.

Key-words:  Laser-arc hybrid welding; Neural network; Genetic algorithm; Value of symmetry

1. Introduction

Due to the nonlinearity, time-varying, and strong coupling of multiple parameters in laser-arc welding, any change in the parameters will affect the welding quality, especially the weld shape. It is difficult for us to accurately establish the above mathematical model.

To gain weld bead with high quality during the automatic welding process, it is important to build the relationship between welding process parameters and weld bead section dimensions. There are two main methods used by scholars around the world. The first one is applying the regression analysis method. Datta et al. [¹] apply multiple linear regression (MLR) to research the relationship between welding parameters and deposition area and the volume of welding bead in submerged arc welding. Murugan and Gunaraj [²] applies multiple nonlinear regression (MNR) to study the connection between the main welding bead dimensions and welding parameters. Yang et al. [³] applies partial least squares regression (PLSR) to simulate the welding bead shape. They obtain the functional relationship between the welding bead section dimensions (weld depth, weld width, weld reinforcement) and welding parameters. However, the dimensions predicted can’t well describe the welding bead section outline integrally. The second method is using neural networks which can solve complicated nonlinear problems to simulate the welding bead shape. Li et al. [⁴] proposes adaptive compensation neural networks to study the nonlinear relation between the main welding bead dimensions and welding parameters. Zhang et al. [⁵] and Ridings et al. [⁶] apply BP neural networks to study the formation of welding beads and the choosing of welding parameters. They all get the neural model between the main dimensions of the welding bead and welding parameters and the error precision is pretty high. However, the same problem is that the dimensions predicted can’t well describe the concrete welding bead shape.

To further study the optimization of welding parameters based on the symmetry of weld section shape, we need to get the left side dimensions and the corresponding right side dimensions of the outline of weld section to calculate its symmetry degree. So a more complex model is needed to predict dimensions (every 15 degrees) on the weld section outline instead of just the weld depth, weld width, and weld reinforcement. These 26 dimensions will be illustrated clearly in following chapters. MLR, MNR, and PLSR methods suffer from multicollinearity problems when multi-dimensional predictor variables are highly correlated, leading to model instability and inaccurate prediction results. The neural network has strong fault tolerance and robustness and can self-learning and self-adaptation, so it has been applied in many fields. However, the over-fitting problem can easily occur when using multiple parameters without a large amount of training data. Therefore, many scholars have adopted different methods to improve and optimize the over-fitting problem. Yang et al. [⁷] proposed a fast adaptive online gradient descent algorithm to solve the over-parameter problem of neural networks. The adopted adaptive strategy only adjusts the learning rate based on the historical gradient and training loss values, while the acceleration strategy is the heavy-ball momentum used to accelerate the training of the deep model. Zhang et al. [⁸] explored two potential training strategies to address the over-fitting problem in AF detection. The first one uses the Fast Fourier transform (FFT) and a filter based on the Hanning window to suppress the influence of individual differences. The other is to train the model on wearable Electrocardiograph (ECG) data instead of traditional ECG data to improve the robustness of the model. Another approach is to apply optimization algorithms to optimize neural networks, such as genetic algorithms and particle swarm optimization [⁹-¹¹]. We intend to apply the genetic algorithm (GA) to optimize the BP neural networks to get a high prediction accuracy model. However, the neural network is trained once with the training data for each individual, so with a large population and slow optimization speed, it takes a relatively long time to get the final neural model. Given the above problems, the MPGA with strong global optimization ability and fast optimization speed [¹²] was used to replace the genetic algorithm (GA). Many scholars have applied the MPGA in many different fields. Wang et al. [¹³] applied the MPGA to optimize an improved Stanley controller to obtain better tracking performance of a two-wheel tractor. Jingcheng Wang et al. [¹⁴] proposed an MPGA program to determine the directional design of wind speeds. The results of the MPGA program can significantly improve the effect of the sector-by-sector method. Zhou et al. [¹⁵] propose a train-set circulation optimization model to minimize the total connection time and maintenance costs and describes the design of an efficient multiple-population genetic algorithm (MPGA) to solve this model.

The choice of initial weight and threshold will affect the training speed and precision of the neural network. Improper selection of initial weights and thresholds may lead to oscillations or non-convergence in the training process, which will affect the final training result. So taking the initial weights and threshold as the individual population in MPGA, a highly accurate neural network can be obtained with the optimization process of MPGA to predict the weld bead section shape. Using the optimized neural network model, the welding section shape under different welding parameters can be predicted, and then the influence of welding parameters on the weld shape of different welding joints can be studied. This model can greatly reduce the number and cost of welding experiments and has great significance for the study of hybrid welding.

2. Establishing the BP Neural Model Optimized with MPGA

The process of optimizing the neural network with MPGA is shown in Figure 1.

Figure 1
The process of optimizing the BP neural network.

According to the above schematic diagram, the topological structure of the BP neural network is first determined based on the input parameters (laser power, welding current, welding gap, welding Angle, and welding bluntness) and output parameters (26 dimensions of the weld section). Then, the weights and thresholds of the BP neural network were randomly initialized and encoded into binary numbers. In MPGA, this string of binary numbers is treated as an individual chromosome in the population. Finally, using the training and testing data, the prediction error is calculated as the fitness function value of each individual. Through the optimization process of MPGA, as shown in Figure 2, a model with higher prediction accuracy can be obtained.

Figure 2
The process of MPGA.

2.1. The topological structure of BP neural networks

A three-layer neural network consisting of the input layer, hidden layer, and output layer, is applied to model the relationship between the welding parameters and dimensions of the welding bead section.

The laser-arc welding parameters are welding current, laser power, welding angle, welding gap and welding blunt as the parameters (X=(I, P, α, d, D)) of input layer, so the number of neurons of input layer n₁ is 5. We take the dimensions of the weld section every 15 degrees which are 24 dimensions in total as the output parameters. However, there is always welding penetration during the butt joint process, so we measure 2 more dimensions shown in Figure 3. 26 dimensions of weld bead section are chosen (Y=(L1, L2, L3,........L25, L26)) as the parameters of output layer, so the number of neurons of output layer n₃ is 26. The number of neurons in hidden layer n₂ can be calculated to be 11 according to the Equation 1.

Figure 3
The schematic diagram of the 2 dimensions added.

$n_2={2\times n}_1+1$ (1)

Based on the above, a 3-layer neural network with a topological structure 5-11-26 should be built to predict the welding bead section dimensions shown in Figure 4.

Figure 4
The topological structure of prediction model.

The number of connection weights of the network is $5\times 11+26\times 11=341$. The number of thresholds of the network is $11+26=37$. The specific number of connection weights and thresholds in each layer is shown in Table 1.

Table 1
The number of weights and threshold values.

Connection Weight between input and hidden layer	Threshold of hidden layer	Connection weight between hidden and output layer	Threshold of output-layer
55	11	286	26

2.2. The Training of BP neural network and testing of error

2.2.1. The initialization and coding of weights and thresholds

According to the Table 1, there are 378 (55+11+286+26=378) weights and thresholds in total. Initialize all the values between [-0.5,0.5]. As the initial weights and thresholds have a significant effect on the final training result of the BP neural network, put them into a line as the optimization parameters of MPGA. The string is shown in Figure 5.

Figure 5
The string of initial weights and threshold.

2.2.2. The training of BP neural network

24 sets of hybrid welding test data were randomly selected as the training data of the neural network. The training of the neural network is the process of continuously modifying the internal values of the weights and thresholds according to the input hybrid welding parameters and the dimensions of the weld bead section so that the output error of the network dimension is smaller and smaller. Set the learning objective as 0.01. The largest times of training are 300 times. The learning rate is 0.1.

After the training of the network, the 25th to 28th groups of hybrid welding test data are used for testing. The four groups of welding process parameters are imported into the trained neural network to obtain the predicted dimensions which will be compared with the test data to calculate the error.

2.3. Optimization of the BP neural network with MPGA

2.3.1. The initialization of population

According to the structure of the three-layer BP neural network 5-11-26 and the way of initialization of weights and thresholds, each value of connection weights and thresholds should be coded into 10-bit binary digits. Connect all the binary digits as an individual in the population of MPGA. The length of an individual is 3780 of which 1st to 550th are the codes of weight between the input and hidden layer and 551st to 660th are the codes of the threshold of the hidden layer and 661st to 3520th are the codes of connection weight between hidden and output layer and 3521st to 3780th are the codes of the threshold of hidden and output layer. The individual chromosome is shown in Figure 6.

Figure 6
The schematic diagram of individual chromosome.

Set the population quantity as 3 and the size of each population as 50. The initialization of populations in MPGA is shown in Figure 7.

Figure 7
The schematic diagram of initialization of populations.

2.3.2. The fitness function of individual chromosome

The fitness evaluation of a chromosome measures the final training result for a BP neural network, which is the important basis to the selection, crossover, and mutation operations. The chromosome is encoded into decimal digits which are assigned to the connection weights and thresholds in the BP neural network. After being trained with the set parameters, apply the 25_th to 28_th groups of welding parameters to test the prediction accuracy. The fitness function value of each chromosome can be calculated through Formula 2.

$f=\sum _{i=25}^{28}\sum _{j=1}^{26}\left|D_{ij}-d_{ij}\right|/26/4$ (2)

The $D_{ij}$ is the predicted dimension and the $d_{ij}$ is the measured dimension. $j$ is the j_th dimension of weld bead section. $i$ is the i_th group of welding experiment.

2.3.3. The optimization operations of MPGA

1. Selection operator: this paper adopts roulette wheel selection and the principle of this is shown in Formula 3.

   $P_i=\frac{f_i}{\sum _{i=1}^{50}{f}_i}$(3)

In the formula, $f_i$ is the fitness value of individual $i$. $P_i$ is the probability that individual $i$ is chosen to pass on to next generation.

1. Crossover operator and mutation operator.

After calculating the fitness value of each individual, 2 genetic operators called crossover operator and mutation operator are applied to evolve the individuals. The process of crossover and mutation operator are shown in Figure 8 and 9.

Figure 8
The process of crossover operator.

Figure 9
The process of mutation operator.

1. Immigrant operator.

Each population is independent during the optimization process, but they are connected by the immigrant operator. According to the fitness value, the immigrant operator introduces the best chromosome of a certain population into other populations, thus exchanging chromosomes among the populations. Immigrant operator can effectively solve the local convergence problem and shorten the time of optimization.

2.3.4. Setting the parameters in MPGA

The crossing probability of each population is randomly set between 0.7 ~ 0.9. The mutation probability is randomly set between 0.01 ~ 0.05. The final accuracy of prediction is set to be 0.01 which will determine the end of the optimization process.

3. Laser-arc Hybrid Welding Experiment

3.1. The equipment and materials of welding experiment

In the hybrid welding experiments, the self-developed composite device platform is shown in Figure 10. The Nd: YAG solid-state laser of TrumPF company in Germany and the MIG/MAG welder of Panasonic YD-350AG2HGE with the maximum welding current of 350A are used for paraxial recombination. The laser was focused through a 220 mm focusing mirror to obtain a 0.5 mm diameter spot. The amount of defocus is -2 mm. The protection gas of the metal active-gas welding (MAG) is a mixture of 10%CO2+90%Ar with a flow rate of 17L/min. The test material was 150mm×30mm×6mm low-alloy high-nitrogen steel plate, and the welding was performed by plate butt welding. A stainless steel wire with a diameter of 1.2 mm was used, the dry protrusion length was 12 mm, and the arc welding pitch inclination was 60º. After welding, the weld section was obtained by computer numerical control (CNC) wire cutting. After being etched by 4% nitric acid alcohol solution and polished, the images of the weld bead section are taken and marked the plotting scales with the metallographic microscope.

Figure 10
The platform of hybrid welding.

With the range of welding parameters $D\in \left(\mathrm{2,4}\right)$/mm,$d\in \left(\mathrm{0.1,0.8}\right)$/mm,$\alpha \in \left(\mathrm{30,60}\right)$/degree,$P\in \left(\mathrm{2.3,2.8}\right)$/KW,$I\in \left(\mathrm{200,280}\right)$/A, 32 sets of welding tests were carried out on the above welding platform. After the welding samples were processed, the cross section images of the weld pass were obtained (Figure 11).

Figure 11
The schematic diagram of welding parameter.

3.2. Measure the dimensions of welding bead section in polar coordinate system

3.2.1. the theoretical principle of automatic measuring method

Aiming at the problem that there is a lack of measuring equipment for the measurement of weld bead section dimensions in a polar coordinate system, an automatic measurement method is proposed. The process is as follows:

1. Apply the SOBEL algorithm to get the outline of the welding bead section shown in Figure 12. The text ‘1.6mm ’ above the white line is plotting scale.

   

   Figure 12
   The outline of welding bead section.
   

1. By detecting the leftmost, rightmost, top, and bottom points of the section outline, draw the lines from the leftmost point to the rightmost point, and from the top point to the bottom point. Take the intersection point of the 2 lines as the center point shown in the Figure 13.

   

   Figure 13
   Schematic diagram of getting the center point of section outline.
   

1. Take the center point as the origin point of the polar coordinate and detect the pixel coordinates ($X_i,Y_i$) of points on the section outline every other 15 degree as shown in Figure 14. Detect the leftmost and rightmost ends of the plotting scale and get the pixel coordinates ($x_1,y_1$) ($x_2,y_2$).

   

   Figure 14
   The dimensions of welding bead shape in polar coordinate system.
   

1. According to the pixel coordinates, we can calculate all the dimensions through the Formula 3 to 5.

   $L_i=\sqrt{{X_i}^2+{Y_i}^2}$(3)
   $l=\sqrt{{(x_1-x_2）}^2+{{（y}_1-y_2)}^2}$(4)
   $d_i=\frac{L_i}{l}\times 1.6$(5)

In the formula, ${\mathrm{L}}_{\mathrm{i}}$ is the pixel length of dimension with a certain angle. l is the pixel length of plotting scale and $d_i$ is the measured dimension in polar coordinate system.

3.2.2. Verify the accuracy of automatic measuring method

Based on the laser-arc hybrid welding experiments, we get 32 groups of images of weld cross-section. Using the automatic measuring method proposed in this paper, we can get the dimensions of all the welding samples. Then compared with the dimensions measured with a metallographic microscope to test the measuring accuracy. The welding parameters of 3 randomly selected samples are shown in the Table 2.

Table 2
The welding parameters of randomly selected samples.

Laser power	Welding current	Weld gap	weld angle	weld blunt
/W	/A	/mm	/°	/mm
2400	220	0.2	40	2.5
2600	220	0.2	50	2.5
2500	230	0.1	45	2.75

Since can not measure the dimensions of the weld cross-section at a specific angle with the microscope, we only measured the dimensions (L1, L2, L3, L4) in horizontal and vertical directions shown in Figure 15 to verify the measuring accuracy of the automatic measuring system proposed in this paper.

Figure 15
The schematic diagram of measuring method with microscope.

It can be seen from Table 3 that the automatic measurement method has high measurement accuracy, and the measurement error is within 2.5%. To show the accuracy of the automatic measurement method more vividly, the actual section image of the weld bead is compared with the numerical simulation weld contour picture shown in Figure 16 to 18.

Table 3
The measuring accuracy calculation of automatic measuring method.

Sample 1				Sample 2
Method in this paper		Method with microscope	error	Method in this paper	Method with microscope		error
L1	7.08	6.98	1.4%	7.3	7.25		0.6%
L2	4.12	4.2	1.9%	3.34	3.39		1.5%
L3	1.36	1.35	0.7%	0.93	0.96		3%
L4	3.35	3.42	2%	3.76	3.69		1.9%
Sample 3
Method in this paper			Method with microscope			error
L1	7.38		7.3			1.1%
L2	3.27		3.31			1.2%
L3	1.46		1.43			2.1%
L4	3.71		3.74			0.8%

Figure 16
The comparison with first group of welding parameters.

Figure 18
The comparison with third group of welding parameters.

Figure 17
The comparison with second group of welding parameters.

According to the graphs above, the dimensions measured with an automatic measuring system can well fit the basic section shape of the welding bead. So the measuring method can be used to measure the section dimensions of the weld bead.

4. The prediction of welding bead section dimensions

4.1. Gain the optimized BP neural model

Because of the welding process parameters with different orders of magnitude, the data should be normalized firstly with the code ‘mapminmax’ in MATLAB and then import the experiment data into the neural model to train the BP neural network. 25th to 28th groups are chosen to calculate the error of the trained BP neural network. Take the error as the fitness function of the population individual. Through the process of MPGA optimizing the inner connection weights and threshold values of BP neural networks, an optimal neural model can be gained. The result of the optimized BP neural network is shown in Figure 19.

Figure 19
The fitting result of optimized BP neural network.

4.2. Test the accuracy of dimensions prediction of optimized BP neural network

Apply the left 3 groups of welding parameters shown in Table 4 to test the predicting accuracy of the optimized BP neural network. Input the normalized welding parameters shown in Table 5 into the neural model to get the dimensions of the weld bead section and then compare them with the measured dimensions to calculate the accuracy shown in Table 6 to 8.

Table 4
The 3 groups of welding parameters.

Laser power	Welding current	Weld gap	weld angle	weld blunt
/W	/A	/mm	/°	/mm
2600	240	0.2	40	2.5
2400	240	0.6	40	2.5
2500	250	0.4	45	2.75

Table 5
The 3 groups of welding parameters normalized.

Laser power	Welding current	Weld gap	weld angle	weld blunt
/W	/A	/mm	/°	/mm
0.5	0.91	-0.667	0.91	0.5
0.5	0.73	0.67	0.91	0.5
-0.5	0.91	0.67	0.91	0.5

Table 6
The predicted outcomes with the first group of welding parameters.

	measured value /mm	Predicted value /mm	Error %		measured value/mm	Predicted value/mm	Error %
Spot 1	1.93	2.07	7	Spot 14	3.09	2.84	8
Spot 2	1.89	2.12	12	Spot 15	1.93	2.19	13
Spot 3	1.91	2.25	18	Spot 16	1.51	1.71	13
Spot 4	2.11	2.4	14	Spot 17	1.28	1.32	3
Spot 5	2.48	2.65	7	Spot 18	1.1	1.26	8
Spot 6	4.95	5.21	5	Spot 19	0.99	1.16	17
Spot 7	5.26	5.26	0	Spot 20	0.94	1.1	17
Spot 8	5.08	5.01	1	Spot 21	0.94	1.15	22
Spot 9	3.44	3.72	8	Spot 22	0.95	1.15	21
Spot 10	3.02	2.87	5	Spot 23	1	1.14	14
Spot 11	2.73	2.77	1	Spot 24	1.17	1.08	8
Spot 12	2.66	2.82	6	Spot 25	1.46	1.36	9
Spot 13	2.79	2.86	3	Spot 26	2.36	2.24	5

Table 8
The predicted outcomes with the third welding parameters.

	Measured value /mm	Predicted value /mm	Error %		measured value/mm	Predicted value/mm	Error %
Spot 1	3.01	3.13	4	Spot 14	3.51	3.16	10
Spot 2	2.94	2.64	10	Spot 15	1.8	2.03	13
Spot 3	3.07	3.07	0	Spot 16	1.38	1.3	6
Spot 4	4.2	4.31	3	Spot 17	1.12	1.13	1
Spot 5	5.69	5.32	7	Spot 18	0.97	1.02	5
Spot 6	6.76	6.53	3	Spot 19	0.91	0.94	3
Spot 7	6.95	6.55	6	Spot 20	0.85	0.89	5
Spot 8	6.84	6.35	6	Spot 21	0.91	1.08	18
Spot 9	6.16	6.08	1	Spot 22	1.01	1.06	5
Spot 10	3.6	3.51	3	Spot 23	1.15	1.4	21
Spot 11	3.24	3.45	6	Spot 24	1.42	1.49	5
Spot 12	3.16	2.96	6	Spot 25	1.84	1.66	10
Spot 13	3.25	3.03	7	Spot 26	3.22	3.48	8

Table 7
The predicted outcomes with the second welding parameters.

	measured value /mm	Predicted value /mm	Error %		measured value/mm	Predicted value/mm	Error %
Spot 1	3.3	3.15	5	Spot 14	3.54	3.34	6
Spot 2	3.04	3.03	0	Spot 15	2.11	1.88	11
Spot 3	3.12	3.13	0	Spot 16	1.76	1.89	7
Spot 4	3.7	3.88	5	Spot 17	1.56	1.87	20
Spot 5	4.72	4.22	11	Spot 18	1.46	1.29	11
Spot 6	6.86	6.91	1	Spot 19	1.4	1.22	12
Spot 7	7.21	6.88	5	Spot 20	1.35	1.45	7
Spot 8	6.93	6.77	2	Spot 21	1.34	1.48	10
Spot 9	4.2	4.42	5	Spot 22	1.46	1.71	17
Spot 10	3.13	3.01	4	Spot 23	1.59	1.59	0
Spot 11	2.73	3.06	12	Spot 24	1.79	1.86	4
Spot 12	2.63	2.98	13	Spot 25	2.11	1.94	8
Spot 13	2.84	3	6	Spot 26	3.75	3.35	11

The results illustrate that the predicting errors are under 0.5mm and the average relative error is under 10%. The largest relative error is 22% for the reason that the dimension of that spot is quite small only about 0.94mm of which the error is 0.25mm. Considering the measurement error, the optimized BP neural networks can well predict the welding bead dimensions.

4.3. Simulating the welding bead outline curve

To visually display the prediction results, firstly, according to the predicted and measured dimensions, the weld section dimensions in polar coordinates are converted into dimensions in a rectangular coordinate system. Then the weld section profile is fitted by using the converted dimensions. The fitted section profile and the real weld section are shown in Figure 20-22. The figures show that the predicted curve fits well with the measured curve except for some points.

Figure 20
Comparison between the predicted welding bead shape curve and that from experiment (sample 1).

Figure 22
Comparison between the predicted welding bead shape curve and that from experiment (sample 3).

Figure 21
Comparison between the predicted welding bead shape curve and that from experiment (sample 2).

4.4. Calculate the value of symmetry of welding bead section

The degree of symmetry of the left and right sides of the weld section outline is used as the standard to judge the appearance of the weld. The absolute value of the mean difference between the dimensions on the left and the dimensions on the right is used as the good condition of the symmetry of each point. The smaller the difference, the better the symmetry. The schematic diagram of a serial number of weld section dimensions is shown in Figure 23.

Figure 23
Schematic diagram of serial number of weld section dimensions.

The degree of symmetry of weld bead section outline can be calculated with the Formula 6.

$$\begin{array}{l}sym=\frac{\left|d_1-d_{1\text{5}}\right|+\left|d_2-d_{1\text{4}}\right|+\mathrm{......}\left|d_{\text{7}}-d_{\text{9}}\right|}{6}\\ \mathrm{...........}+\frac{\left|d_{1\text{6}}-d_{26}\right|+\left|d_{1\text{7}}-d_{25}\right|+\mathrm{......}\left|d_{19}-d_{21}\right|}{6}\end{array}$$ ₍₆₎

According to the table 6 to 8, we apply the predicted and measured dimensions to calculate the degree of symmetry of the 3 test samples. The results are shown in the table below.

According to the mean value of symmetry degree in Table 9, it can be found that the absolute error between the predicted and the measured degree of symmetry is less than 0.04mm. Due to the small base of degree of symmetry, a slight deviation may cause a large relative error. The predicted degree of symmetry of the four groups of samples from low to high is sample 1, sample 3, and sample 2, which is consistent with the actual measured degree of symmetry. Therefore, this prediction model can be used as an evaluation model of weld section appearance which can be applied to further research on optimizing the welding parameters based on the degree of symmetry of the weld section outline.

Table 9
The value of symmetry of welding bead section.

Average value of symmetry with predicted dimensions/mm	Average value of symmetry with measured dimensions/mm	Error/mm	Relative error/%
0.185	0.203	0.023	12%
0.368	0.338	0.030	8%
0.262	0.226	0.036	15%

5. Conclusion

This paper aims to develop the prediction model for the symmetry of the weld section outline, so the prediction model of the 26 dimensions of the weld bead section should be built. For this purpose, a series of experiments were performed with the welding parameters welding current, laser power, welding gap, welding angle, and welding blunt. Because of lacking effective measuring tools, this paper developed an automatic measuring system by establishing a polar coordinate of the weld topography to efficiently complete the dimensional measurement of the weld contour. Results indicate that the measuring method in this paper cannot accurately describe all the details of the weld topography, but it can present the weld topography characteristics in detail through the simulation of measurement data and the comparison of actual weld topography pictures. The method can greatly reduce the manual labor of measuring the weld section dimensions.

BP neural network is applied to build the prediction model for the 26 dimensions. It is known that the initial values of weights and threshold can have a great effect on the stability of training, rate of convergence, and the accuracy of prediction, so the initial values of weights and threshold are taken as the individuals of the population in MPGA optimization algorithm to gain a predictive model with high accuracy. The results show that the prediction errors of dimensions are under 0.5mm and the average relative error is under 10%. The method using MPGA to optimize the initial values of weights and thresholds can effectively solve the over-fitting problem of neural networks with multiple input and output parameters.

With the 26 dimensions predicted, the symmetry value of the weld section outline can be calculated. The results show that the symmetry values predicted can well describe the quality of weld section morphology, which can be used for further study about the optimization of welding process parameters based on the quality of welding bead morphology.

• How to cite: Hong Y, De Ocampo AL, Tan W, Zhong M, Li S. The prediction of laser-arc hybrid welding bead shape basing on multiple population genetic algorithm and neural networks. Soldagem & Inspeção. 2024;29:e2912. https://doi.org/10.1590/0104-9224/SI29.12
• Funding
  National Youth Science Foundation Project Of China (51305044)

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Publication Dates

• Publication in this collection
  13 Dec 2024
• Date of issue
  2024

History

• Received
  11 Apr 2024
• Accepted
  02 Sept 2024