Laser–Arc Welding Adaptive Model of Multi-Pre-Welding Condition Based on GA-BP Neural Network

Abstract

In large welding structures, maintaining a uniform assembly condition and machined dimension in the pre-welding groove is challenging. The assembly condition and machined dimension of the pre-welding groove significantly impact the selection of the welding parameters. In this study, laser–arc hybrid welding is used to perform butt welding on 6 mm Q345 steel in various assembly conditions, and we propose an adaptive model of the BP neural network optimized by a genetic algorithm (GA) for laser–arc welding. By employing the GA algorithm to optimize the parameters of the neural network, the relationship between the pre-welding groove parameters and welding parameters is established. The mean square error (MSE) of the GA-BP neural network is 0.75%. It is verified via experiments that the neural network can predict the welding parameters required to process a specific welding morphology under different pre-welding grooves. This model provides technical support for the development of intelligent welding systems for large and complex components.

1. Introduction

In large-scale welding structures, such as in shipbuilding, nuclear power, and other industries, factors like the assembly accuracy and the machined size of the pre-welding groove cause inconsistencies in the pre-welding structure. This requires a heat source with a wide welding window to accommodate these variations. While a single arc heat source offers good bridging abilities, it has a limited penetration capacity [1]. On the other hand, a single laser heat source has excellent penetration but lacks sufficient bridging capabilities [2]. Laser–arc welding was first invented by Steen in 1980 [3]; it merges the advantages of both laser and arc welding [4], resulting in a process that is more adaptable and offers a wider process range. It is suitable for the automated and intelligent welding of large and complex components. Shipyards, such as those at Fincantieri and STX, have adopted laser–arc welding for shipbuilding [4], and laser–arc welding is considered the ideal joining method for large-scale structures like ships [5].

In order to effectively predict and optimize physical quantities such as the welding current and laser power, researchers have begun to use a variety of methods to develop mathematical models of the relationship between the pre-welding structure, the welding parameters, and the weld morphology. Tarng et al. [6] used Taguchi’s method to analyze the effect of each welding parameter on the weld morphology in tungsten arc welding and predicted the optimal welding parameters. Lee et al. [7] predicted the welding speed and welding current for submerged arc welding using Taguchi’s method of fuzzy logic. Cao et al. [8] employed the response surface method, with the welding current, electrode pressure, and welding time as inputs and the weld core and shear strength as outputs, using a genetic algorithm to optimize the process parameters. They also predicted and verified the model’s accuracy. Liu et al. [9] predicted the shear strength and weld width by using the laser power, welding speed, and defocus as inputs and the weld width and shear strength as outputs. Zhou et al. [10] optimized the process parameters of CFRP metal laser welding using residual regression. Yu et al. [11] used logistic regression to predict the weld quality in resistance spot welding.

As the size and complexity of data continue to grow, the limitations of traditional statistical methods become increasingly apparent, particularly when handling non-linear, multi-dimensional, and complex relational data. The BP neural network, a powerful machine learning algorithm, offers significant advantages in statistical mathematical modeling, thanks to its superior self-learning abilities and proficiency in non-linear modeling. Y. Chang et al. [12] predicted the weld profile with an error of less than 0.1 mm by using the welding current, welding speed, torch angle, and real-time molten pool width as inputs to the neural network, while the three parameters of the weld profile served as outputs. H. Wang et al. [13] predicted the cross-sectional profile of rivet welding by using the welding current, welding speed, laser power, and defocus as inputs, with the rivet welding profile dimensions as the output. Manvatkar et al. [14] predicted the cross-sectional shape of friction stir welding using inputs such as the shoulder radius, tool rotational speed, pin radius, pin length, welding speed, and axial pressure. They successfully predicted the peak temperature, total torque, traverse force, bending stress, and maximum shear stress, optimizing the friction stir welding process. Yilikal et al. [15] developed a three-layer neural network, using the current, dry elongation, voltage, and speed as inputs and the tensile strength, hardness, and weld width as outputs, to predict the tensile strength and hardness under different process parameters. Navid et al. [16] used neural networks to predict the hardness and grain size in the friction stir welding of pure titanium. These studies demonstrate the excellent predictive abilities of neural networks in forecasting the necessary welding parameters for welds.

Optimization algorithms play a crucial role in the training processes of BP neural networks, which are typical feed-forward neural networks that minimize the loss function by updating the network weights using the gradient descent method. However, the traditional gradient descent method can encounter several issues in practical applications, such as local minima, slow convergence, and susceptibility to saddle points. Therefore, it is essential to introduce optimization algorithms to enhance the training effectiveness and convergence performance of BP neural networks. Wang et al. [13] employed a genetic algorithm to optimize the convergence speed and prediction accuracy of the neural network. Liu et al. [17] predicted the number of porosities and their average area in stainless-steel double-laser-welded joints by using a BP neural network optimized with a genetic algorithm. Xiong et al. [18] optimized the design of the experimental parameters using the non-dominated sorting genetic algorithm II. Lei et al. [19] applied principal component analysis (PCA) and a genetic algorithm (GA)-optimized multi-information fused neural network to predict the forming shape of the weld in real time from molten pool images. Meng et al. [20] predicted the wire feeding speed and welding speed using a BP neural network optimized by a genetic algorithm. Liu et al. [17] used a BP neural network optimized by a genetic algorithm to predict the weld porosity, as well as the number of pores and their average area. Zhao et al. [21] employed a BP neural network optimized by a genetic algorithm to predict the tensile strength in the ultrasonic welding of copper wire and aluminum alloy. DEM is a useful instrument to successfully design, optimize, or simply analyze systems and equipment for granular materials in many applications where interparticle forces play a key role [22]. Genetic algorithms offer significant advantages over traditional optimization algorithms, particularly in terms of their global search capabilities, adaptability, and the ability to handle high-dimensional problems. They excel in multi-objective optimization and do not require gradient information. Genetic algorithms are highly effective in addressing complex, nonlinear, large-scale, high-dimensional, and both unconstrained and constrained optimization problems.

In this study, a mathematical model is developed to establish the relationship between the pre-welding groove parameters, welding morphology, and welding parameters using a BP neural network optimized by a genetic algorithm. A Q345 steel plate with a thickness of 6 mm is welded under different assembly conditions and machined dimensions using laser–arc hybrid welding to produce the specified welding morphology.

2. Experimental Section

2.1. Experimental Materials

In this study, the experimental materials were 6-mm-thick Q345 with the dimensions of 300 mm × 150 mm × 6 mm and a 1.2-mm-diameter ER50-6 filler wire, as shown in

Table 1. Chemical compositions (%) of the base metal and the filler wire.

Material	C	Si	Mn	Cu	Ni	Cr	P	S
Q345	0.20	0.55	1.70	-	-	0.01	0.045	0.030
ER50-6	0.077	0.90	1.45	0.50	0.015	0.15	0.025	0.025

. The surface oxide film was removed through machine grinding, followed by cleaning with alcohol to ensure that the weld surface was free from oil and oxide film contamination.

2.2. Experimental Equipment and Process

Based on the advantages of strong bridging capabilities and high penetration capabilities, laser–arc hybrid welding was adopted in this study. The experimental setup, as depicted in Figure 1, reflected a low-power pulsed laser–arc hybrid welding process. The welding torch was perpendicular to the base metal, with the welding torch and laser head positioned at a 45° angle relative to each other. The pulsed laser had a wavelength of 1064 nm, a rectangular waveform, a focal length of 150 mm, and a spot diameter of 1 mm. This setup included a low-power pulsed laser (XL-650WF, Xinglai Laser, Guangzhou, China) and a Lorch Pulse GMAW welding power source (S8-Speed) (Lorch, Auenwald, German). The laser head and welding torch were fixed on a FANUC R-30iA welding robot (FANUC Corporation, Oshino, Japan) using a fixture. A base plate was installed to ensure the mismatch, gap, and base angle, as illustrated in Figure 2. The root face (RF) is the thickness of the bottom of the V-groove, the gap (G) is the distance from the base at the start of the weld, and the mismatch (M) is the vertical distance between the bottom of the two plates, as shown in Figure 2c. The base angle (BA) is the same paraxial angle between two plates in the welding direction at the start of the weld, and BA is equal to α plus β, as illustrated in Figure 2b. BA indicates the sharpness of the gap changes. To acquire the optimal welding parameters under different welding groove conditions, three different grooves were machined. Each groove had an angle of 30°, with the thicknesses of the root face being 1.5 mm, 2 mm, and 2.5 mm, respectively, as shown in Figure 3.

In the laser–arc welding process, several parameters affect the morphology and quality of the welding joint, such as the shielding gas, gas flow rate, distance between the laser and arc (DLA), torch inclination, and defocusing amount. For a given material, the optimal welding morphology can be achieved by using specific parameters. The fixed parameters are as follows: 0 mm defocus amount, 1 mm DLA, protective gas flow between 15 and 20 L/min, and air supply consisting of Ar (80%) + CO₂ (20%). The maximum penetration is attained when the welding torch is held vertically, with the arc positioned in front of the laser; the angle between the laser and the arc is 45 degrees, and the nozzle-to-plate distance is 15 mm. The primary factors influencing the welding morphology are the welding current, welding speed, and laser power. This study focused on investigating the process parameters required for these three factors under different assembly conditions.

In

Table 2. Experimental design and results.

No.	RF	Gap	BA	Mismatch	BR	BW	I	V	P
1	1.5	0	180	0	1.37	4.21	240	10	290
2	1.5	1	180	1	0.50	2.39	210	10	290
3	1.5	2	180	0.5	0.54	1.98	150	10	0
4	2	0	180	1	2.30	3.83	240	10	470
5	2	1	180	0.5	1.08	3.38	210	10	290
6	2	2	180	0	0.54	2.71	160	10	0
7	2.5	0	180	0.5	2.12	3.92	240	10	470
8	2.5	1	180	0	2.03	4.83	210	10	290
9	2.5	2	180	1	1.40	3.07	150	10	290
10	1.5	0	180.004	0	1.62	4.11	215	10	290
11	1.5	1	180.004	1	1.33	3.79	190	10	290
12	1.5	0	180.006	0.5	1.04	3.61	210	10	470
13	2	0	180.004	1	1.89	3.24	255	10	290
14	2	1	180.004	0.5	1.17	3.47	185	10	0
15	2	0	180.006	0	0.72	3.52	190	10	0
16	2.5	0	180.004	0.5	−2.21	0	240	10	552
17	2.5	1	180.004	0	1.22	3.70	190	10	0
18	2.5	0	180.006	1	−2.26	0	230	10	552
19	1.5	1	179.996	0	0.95	3.74	240	10	470
20	1.5	2	179.996	1	0.27	2.71	210	10	290
21	1.5	2	179.994	0.5	1.13	3.83	220	10	290
22	2	1	179.996	1	0	0	245	10	374
23	2	2	179.996	0.5	1.22	3.20	210	10	290
24	2	2	179.994	0	0.21	1.62	220	10	390
25	2.5	1	179.996	0.5	−1.71	0	240	10	474
26	2.5	2	179.996	0	0.63	2.98	220	10	290
27	2.5	2	179.994	1	1.31	2.93	240	10	470
28	1.5	0	180	0	1.30	3.82	260	10	290
29	1.5	1	180	1	0.80	2.44	210	10	290
30	1.5	2	180	0.5	0.77	2.10	145	10	0
31	2	0	180	1	1.80	3.77	255	10	470
32	2	1	180	0.5	1.20	3.55	220	10	290
33	2	2	180	0	0.80	2.33	150	10	0
34	2.5	0	180	0.5	1.22	3.88	260	10	470
35	2.5	1	180	0	1.85	4.55	210	10	290
36	2.5	2	180	1	0.95	3.66	145	10	290
37	1.5	0	180.004	0	1.22	4.21	220	10	290
38	1.5	1	180.004	1	1.11	3.85	180	10	290
39	1.5	0	180.006	0.5	0.95	3.75	190	10	470
40	2	0	180.004	1	1.44	3.56	250	10	290
41	2	1	180.004	0.5	1.20	3.66	180	10	0
42	2	0	180.006	0	1.13	3.48	185	10	0
43	2.5	0	180.004	0.5	0.95	3.11	240	10	552
44	2.5	1	180.004	0	1.22	3.70	180	10	0
45	2.5	0	180.006	1	1.45	4.23	220	10	552
46	1.5	1	179.996	0	0.96	4.11	240	10	470
47	1.5	2	179.996	1	0.52	3.85	210	10	290
48	1.5	2	179.994	0.5	0.85	3.83	220	10	290
49	2	1	179.996	1	0.75	3.95	240	10	374
50	2	2	179.996	0.5	0.22	3.13	210	10	290
51	2	2	179.994	0	0.75	3.65	220	10	390
52	2.5	1	179.996	0.5	0.94	3.88	250	10	474
53	2.5	2	179.996	0	0.75	3.95	230	10	290
54	2.5	2	179.994	1	1.11	4.33	220	10	470

, 1–9 refer to orthogonal experiments where the gap does not change; 10–18 focus on the case of a progressively larger gap, while 19–27 refer to the case of a progressively smaller gap. Meanwhile, 28–54 repeated 1–27. As the gap gradually changes, both the back reinforcement height and back width also vary. Therefore, the back reinforcement height (BR) and back width (BW) at the midpoint of the weld in each section represent the overall back height and back width of the entire weld.

3. GA-BP Neural Network Modeling

The GA is widely utilized to enhance the performance of BP neural networks. The GA, inspired by genetic mechanisms and biological evolution, operates as a stochastic search method. It employs selection, crossover, and mutation operations to identify individuals with the best fitness values in each iteration, thereby optimizing the connection weights and thresholds within the neural network. This approach effectively narrows the search space, ultimately improving the prediction accuracy and robustness of the model. BP neural networks can suffer from slow convergence and a tendency to become stuck in local optima, particularly with small training data sets. To address these issues, the GA-BP neural network utilizes the global search capabilities of the genetic algorithm (GA) to identify the optimal initial weights and thresholds. To develop an adaptive model for weld grooves with gaps, root faces, and base angles, we use the GA to optimize the weights and thresholds of the BPNN. The optimized initial weights and thresholds are then used to train the BPNN. The flowchart of this algorithm is shown in Figure 4.

3.1. BP Neural Network Structure

Since the BP neural network model is designed as a controller for the laser–arc welding process, an adaptive welding model must account for variations in the root face, mismatch, root face, and base angle, which will be used as the four input-layer neurons. Additionally, the back width and back reinforcement will be included as two input-layer neurons to ensure that we obtain an ideal weld morphology.

The trial-and-error method was employed to determine the optimal number of layers and neurons in the hidden layer. Various configurations were tested by adjusting the number of neurons and layers in the hidden layer to achieve the best performance for the neural network. After numerous iterations, it was determined that the optimal configuration consisted of two hidden layers, each containing four neurons.

The structure of the neural network, as shown in Figure 5, consists of a 4-layer feed-forward network. It includes 6 neurons in the input layer, representing the root face, gap, mismatch, base angle, back reinforcement, and back width. The output layer has 3 neurons, corresponding to the welding speed, welding current, and laser power.

3.2. Genetic Algorithm (GA)

The genetic algorithm (GA) is a global search technique that seeks the optimal solution to an optimization problem by simulating the genetic evolution of organisms. It maintains a population of potential solutions and evolves this population through selection, crossover, and mutation operators, similar to natural evolutionary processes. The GA iteratively searches for a globally optimal solution, with each iteration representing a cycle in biological evolution, continuing until the algorithm’s termination criteria are satisfied.

3.2.1. GA Design

• Population Initialization

The individual coding method employs real number encoding, where each individual is represented as a string of real numbers. This string comprises four components: the connection weights between the input and hidden layers, the threshold values of the hidden layer, the connection weights between the hidden and output layers, and the threshold values of the output layer. Each individual encapsulates all the weights and thresholds of the backpropagation neural network (BPNN). Given a known network structure, this encoding allows for the formation of a neural network with a specified structure, weights, and thresholds.

(1) Coding mode—real number coding. (2) Chromosome length—calculated as the sum of the following components: the number of neurons in the input layer multiplied by the number of neurons in the hidden layer, plus the number of neurons in the hidden layer multiplied by the number of neurons in the output layer, plus the number of neurons in the hidden layer, plus the number of neurons in the output layer. For the BPNN structure proposed in Figure 5, the chromosome length is

6 × 4 + 4 × 4 + 3 × 4 + 4 + 4 + 3 = 63.

2.

Fitness Function

The initial weights and thresholds of the BPNN are derived from the individuals in the GA. After training the BPNN, the predicted output is obtained by minimizing the sum of the squared errors between the actual samples and the predicted outputs. The fitness of each individual is determined by the desired output of the BPNN, calculated using the following formula:

$$F=k{\sum }_{i=1}^n{(Y_i-O_i)}^2$$

(1)

where n represents the number of output nodes in the BPNN; $Y_i$ is the desired output of the i-th node; Oi is the predicted output of the i-th node; and k is a coefficient.

3.

Selection

GA selection operations include methods such as roulette selection, tournament selection, and others. In this paper, we employ the roulette method, where the selection probability P_i for each individual is determined based on the proportional fitness selection strategy as follows:

$$\left\{\begin{array}{c}{f}_i=k/F_i\\ P_i=f_i/\sum _{i=i}^n{f}_i\end{array}\right.$$

(2)

where $F_i$ is the fitness value of the i-th individual, $P_i$ is the selection probability, and n is the population size. Since lower fitness values are preferred, the inverse of the fitness value is used to determine the selection probability before selecting individuals.

4.

Crossover

Individuals in the GA are encoded as real numbers. Consequently, the crossover operation is performed using the real number crossover method, where the k-th chromosome $a_k$ is crossed over with the i-th chromosome at the j-th position as follows:

$$\left\{\begin{array}{c}{a}_{kj}=a_{kj}\times (1-b)+{ a}_{lj}\times b\\ a_{ij}=a_{lj}\times \left(1-b\right)+a_{kj}\times b\end{array}\right.$$

(3)

where b is a random number between 0 and 1.

5.

Mutation

The j-th gene of the i-th individual is selected for mutation, which is carried out as follows:

$$a_{ij}=\left\{\begin{array}{c}{a}_{ij}+\left(a_{ij}-a_{max}\right)\times f\left(g\right); r>0.5\\ a_{ij}+\left(a_{min}-a_{ij}\right)\times f\left(g\right); r\le 0.5\end{array}\right.$$

(4)

where ${a }_{max}$ is the upper bound of gene $a_{ij}$, $a_{min}$ is the lower bound of gene $a_{ij}$, and

$$f\left(g\right)=r_2\times {( 1-g/G_{max} )}^2$$

(5)

where $r_2$ are random numbers, g is the current iteration number, and $G_{max}$ is the maximum number of iterations.

3.2.2. GA Parameters

The initial weights and thresholds of the BPNN are optimized using a genetic algorithm (GA). The population size is set to 20, and the maximum number of generations is initialized to 30. For the genetic operators, the chromosome length is 63, based on the BPNN architecture. The selection operator is the roulette wheel method, and the crossover operator is a single-point crossover, with a crossover probability of 0.9 and a mutation probability of 0.2.

4. Results and Discussion

The weights and thresholds of the BPNN are encoded as individuals in the GA using real number encoding, with each individual representing the complete set of BPNN weights and thresholds. The fitness of each individual is evaluated based on the fitness function, and the GA identifies the optimal individual by applying selection, crossover, and mutation operations. The evolutionary process of the genetic algorithm is illustrated in Figure 6a.

Then, the optimal individuals are decoded as the optimal initial weights and thresholds of the BPNN, and, based on this, the BPNN is trained using the parameters given in Table 2. The desired error of the BPNN is reached after the 27th epoch, and the mean square error (MSE) is 0.75%; when the error of the BPNN is minimized, a final adaptive model is established that correlates the welding parameters, weld morphology, and pre-welded groove. The convergence process of the optimal BPNN is shown in Figure 6b.

4.1. Testing the GA-BP Neural Network

Figure 6c,d illustrate the actual and predicted errors for the laser power and welding current in the GA-BP neural network model. The error of the welding current is under 10 A, as shown in Figure 6c. In the fourth data point of the test set, the difference between the predicted and actual values is significantly larger than in the other cases, where all other predictions have a difference of less than 60 w from the actual values. This can be considered a noise point. The error of the laser power is less than 60 W, as shown in Figure 6d. These results demonstrate that the GA-BP neural network model provides excellent prediction performance.

4.2. Validation of GA-BPNN Through Experimentation

To verify the effectiveness of the laser–arc welding adaptive model, three random assemblies and machined dimensions were designed, as detailed in

Table 3. Verification of experimental design and results.

No.	RF/mm	M/mm	BA/mm	Gap/mm	Experimental Parameters		Desired Geometry Size		Actual Geometry Size
					P/W	I/A	BW/mm	BR/mm	BW/mm	BR/mm
S1	2	0	180	0	450	240	3	0.5	2.82	0.51
S2	1.5	1	180.004	2	0	145	3	0.5	2.91	0.46
S3	2.5	0.5	179.006	1	460	250	3	0.5	3.1	0.43

. Despite the differing groove dimensions, the same weld morphology was required. The gap, mismatch, base angle, and desired final weld morphology dimensions served as the six input neurons for the GA-BPNN. Using the adaptive laser–arc welding adaptive model based on the GA-BPNN, the corresponding outputs were obtained and used to predict the welding process parameters. Validation experiments were then conducted, and the weld seams were wire-cut for metallographic analysis, with Epson scans used to capture the actual weld geometry. The process parameters and results from the validation experiments are presented in Table 3, and the weld cross-section morphology for different machined dimensions and assembly conditions is shown in Figure 7. In the front view and cross-section of sample 1, a biting defect is visible on one side of the weld. In the front view and cross-section of sample 2, the weld appears flawless. In the cross-section and front view of sample 3, a biting defect is observed at the weld.

The results predicted by GA-BP were very close to the experimental results for the training samples. As shown in Figure 8, the correlation coefficient of the training data reached 0.96221, indicating that the fitting effect was excellent. At the same time, the R values of the regression analysis used for the validation data and the test data reached 0.95616 and 0.92376, respectively, indicating that the model is reliable.

5. Conclusions

In this study, Q345 steel was used to verify that laser–arc welding is effective for the welding of various structures along a 300-mm-long weld. Furthermore, the adaptive GA-BP neural network model can predict the required welding parameters under different assembly states and can solve the problem of welding groove fluctuations in large welded structures. The conclusions are as follows.

(1)

An adaptive welding model for flexible laser–arc hybrid welding was developed via a GA-BP neural network. The input layer consists of six neurons, representing the mismatch, gap, base angle, back reinforcement, and back width. The output layer includes three neurons for the welding current, welding speed, and laser power. This model can predict the welding process parameters based on different pre-welding grooves.

(2)

Laser-GMAW can be achieved by adjusting the balance between the laser power and arc power. This adjustment controls the melting penetration of medium–thick mild steel plates under various pre-welding groove conditions.

(3)

The experimental results indicated that the adaptive model based on the GA-BPNN was effective in describing the relationship between the pre-welding structure dimensions, the ideal geometric parameters of weld beads, and the optimized welding parameters to produce the ideal welds.

(4)

The adaptive model established by the GA-BPNN lays the foundation for the adaptive control of pre-welding grooves with variations in the groove dimensions in the welding process.