Using a back propagation neutral network based modeling and heuristic algorithms based optimization technique in activated gas tungsten arc welding process

2. Experimental Set Up

2.1. Equipment and material used

To carry out the experimental tests based on the CCD and BBD design matrixes proposed by RSM, a DIGITIG 250 AC/DC welding machine has been employed (Fig. 1). Furthermore, in this study, Argon (with 99.7% purity) has been used as the shielding inert gas.

AISI316L stainless steel sheets with dimension of 100 mm×50 mm×5 mm have been considered as specimens (Fig. 1). In this study, a combination of Nano oxide fluxes (TiO₂, SiO₂) (+ 99%, 20–30 nm, amorphous) have been used as activating fluxes. Firstly, to assure the powder particle size, FESEM test has been employed (Fig. 2). Figure 3 represents the FESEM results of the oxide-based activating fluxes used which confirmed the Nano-scale claimed by provider. Next, a paste like coating of fluxes prepared by adding a mixture of fluxes (20-grams of TiO₂ and SiO₂) with 20 ml of methanol (as a carrier solvent) using approximately 20 minutes of mechanical, magnetic and ultrasonic mixers (Fig. 4)) [1, 2]. Then, the paste like flux has been applied on the surface of the specimen with a brush and dried before the welding process begins (Fig. 5).

2.2. Response surface methodology (RSM)

Defining a proper experimental design matrix using of which experiments required for modeling and optimization purposes are conducted, is the next step after selecting the main process input variables and their corresponding intervals and levels. In this study, the main process variables and their corresponding intervals and levels have been determined based on the literature survey and preliminary experimental tests using screening procedure. Generally, to facilitate the identification of each individual process variables influences, establish the relations between process input variables and output measures, and determine the optimal levels of input variables in order to get the desired responses (in this study, minimum WBW, maximum DOP, and desired ASR), DOE approach is employed.

There are different approaches in DOE method, among which response surface methodology (RSM) acts as a powerful tool. RSM comprises different designs, including central composite design (CCD) (spherical CCD, rotatable CCD, and etc.), box–behnken design (BBD), and hybrid designs (Fig. 6) [20].

2.3. Determination of adjusting variables and their corresponding intervals and levels

There are different variables affecting the A-GTAW process among which, the most influential ones based on the literature review and screening method used are welding speed (S) and welding current (I). Furthermore, percentage of activating fluxes combination (F) has been considered as a process input variable to achieve the merits of both in this regard [1–3]. Similarly, process quality characteristics including DOP, WBW, and ASR are the most important responses of A-GTAW process. To determine the possible working intervals of each process input variables, welding references studied and some preliminary tests have been carried out [8–15]. The process input variables and their possible intervals and levels have been shown in Tables 1, 2 considered for CCD and BBD designs respectively. Other input variables with trivial effects have been considered at an optimum fixed level. In this study, a CCD’s L₂₀ and a BBD’s L₁₇ matrix have been opted (Tables 3 and 4).

Table 1

Process input variables and their corresponding intervals and levels considered for CCD
Process parameter	Flux combinations ( SiO₂- TiO₂)	Welding current	Welding speed
Symbol	F	C	S
Unit	%	Amps	mm/sec
Interval	0-100	90–130	110–190
Level 1	0-100	90	110
Level 2	25–75	100	130
Level 3	50–50	110	150
Level 4	75 − 25	120	170
Level 5	100-0	130	190

Table 2

Process input variables and their corresponding intervals and levels considered for BBD
Process parameter	Flux combinations ( SiO₂- TiO₂)	Welding current	Welding speed
Symbol	F	C	S
Unit	%	Amps	mm/sec
Interval	25–75	100–120	125–175
Level 1	25	100	125
Level 2	50	110	150
Level 3	75	120	175

2.4. Experimental results

A random order in conducting experiments has been used to increase the accuracy of the experiments. After welding, three types of responses (DOP, WBW, and ASR) have been measured from each specimen (Tables 3 and 4).

Two cross sections on each sample have been made in order to measure DOP, WBW, and consequently ASR. Next, to clearly show DOP and WBW, the cut faces have been polished smoothly and etched (Figs. 7). Then, for taking images an optical microscope has been used (Fig. 7). To determine samples’ DOP and WBW, images have been processed by MIP software (Fig. 7). Results of the measuring process has been illustrated in Figs. 8 and 9.

Table 3

Experimental conditions based on CCD and their corresponding measured outputs
No.	Welding speed (mm/sec)	Welding current (Amp)	Flux combination (SiO₂ - TiO₂)	Depth of penetration (mm)	Weld bead width (mm)	Aspect ratio (AR)
1	130	120	25	5.755	7.693	1.337
2	150	110	50	5.041	7.905	1.568
3	170	100	75	5.367	7.224	1.346
4	170	100	25	3.142	9.466	3.013
5	150	110	50	4.711	7.617	1.617
6	150	130	50	6.827	7.703	1.128
7	170	120	25	3.92	8.425	2.149
8	170	120	75	5.524	5.923	1.072
9	130	100	25	4.873	8.125	1.667
10	150	110	50	4.321	7.92	1.833
11	150	110	50	4.85	7.51	1.548
12	130	100	75	6.356	6.676	1.051
13	150	110	50	4.95	7.847	1.585
14	150	110	100	6.124	5.604	0.915
15	110	110	50	6.254	6.393	1.022
16	150	90	50	4.61	7.778	1.687
17	150	110	50	4.906	7.803	1.591
18	130	120	75	7.894	6.91	0.875
19	150	110	0	3.133	9.985	3.187
20	190	110	50	3.85	7.46	1.938

To relate the process input variables and output responses for CCD and BBD matrixes, regression equations proposed for DOP, WBW, and ASR (Equations 1–6).

DOP = 24.19 + 0.03358×F − 0.381×C + 0.000230×(S×S) − 0.000960×(S×C) + 0.002608×(C×C) (1)

WBW = -28.83 + 0.0549×F + 0.3483×S + 0.1842×C − 0.000628×(F×S) − 0.000526×(S×S) − 0.001340×(S×C) (2)

W/D=-15.39 + 0.1125×S + 0.1634×C + 0.000155× (F×F) -0.000448×(F×S) + 0.000280×(F×C) − 0.000109×(S×S) − 0.000395×(S×C) − 0.000615×(C×C) (3)

DOP = -21.9 + 0.1187×F + 0.425×C − 0.001189×(F×F) − 0.000189×(F×S) + 0.000435×(F×C) + 0.000251× (S×S)- 0.000879×(S×C) − 0.001251×(C×C) (4)

WBW = -97.8–0.1743×F + 0.4264×S + 1.338×C + 0.000561×(F×S) + 0.000761×(F×C) − 0.001564× (S×S)

+ 0.000381×(S×C) − 0.00630×(C×C) (5)

ASR = e^− 6.60 × F^− 0.2853 × S ^2.005 × C ^− 0.392 (6)

Table 4

Experimental conditions based on BBD and their corresponding measured outputs
No.	Welding speed (mm/sec)	Welding current (I)	Flux combination (SiO₂ -TiO₂)	Depth of penetration (mm)	Weld bead width (mm)	Aspect ratio (ASR)
1	50	175	100	3.96	6.21	1.57
2	50	150	110	4.65	7.66	1.65
3	50	150	110	5.10	7.58	1.48
4	50	125	120	6.16	6.12	0.99
5	50	125	100	4.84	5.07	1.05
6	75	125	110	5.65	5.74	1.02
7	50	150	110	4.79	8.26	1.72
8	75	150	120	4.95	7.62	1.54
9	50	175	120	4.42	7.64	1.73
10	50	150	110	4.83	7.91	1.64
11	25	125	110	4.58	6.75	1.47
12	75	175	110	3.64	7.82	2.15
13	25	175	110	3.04	7.44	2.44
14	75	150	100	4.03	6.61	1.64
15	50	150	110	4.68	7.96	1.70
16	25	150	120	3.63	7.57	2.08
17	25	150	100	3.15	7.33	2.32

3. Back Propagation Neural Network (Bpnn)

In order to relate a set of input-output parameters in a system (a manufacturing process such ) different procedures are being employed among which ANNs are the most extensively used ones. ANNs are embrace of a set of connecting processing units named neurons/nodes, organized in each layer (input, hidden and output). An illustration of a perceptron is shown in Fig. 9 (a), where each input variable (defined as x_i) is related with a weight (w_i) which indicates a portion of the input variable to the neuron for processing. Furthermore, b is the bias and y the output signal.

Fig 9 (a), represents a linear perceptron’s inputs (x₁-x_n) combination. Next, a signal is obtained and transferred using function (f) in order to obtain the output signal (y) [17, 18].

Different structures for ANN have been proposed among which multi-layer perceptron (MLP) has been extensively used due to its ability to solve different problems (including non-linear separable/continuous). MLP networks embraces an input layer, hidden layer/s (one or more), and an output layer (Figure 9 (b)). In the training stage, a supervised way is used to determine the biases and weights, based a set of input-output data pairs, which allows the MLP to learn the input-output parameters relations (in this study, process input variables and output responses). In BPNN, an algorithm (back propagation) is employed in which error of each MLP’s input-output pair is calculated and then propagated from the last (output) layer to the first (input) layer, adjusting the biases and weights of the MLP network to the error devoted by its neuron proportionally, is used [15]. The details in this regard are well documented in Refs. [16, 19].

Commonly, the architecture of ANN models is determined based on trial and error. Whereas, in this study in order to eradicate this error, PSO algorithm has been used to determine the proper BPNN’s architecture. The hidden layers’ number was varied from 1 to 3; hence a 3 (number of process input variables)–n₁–n₂–n₃–3 (number of process output characteristics) structure was constructed; where the number of neurons/ nodes for the 1st to 3rd hidden layers are n₁, n₂, and n₃ respectively. The training stage acts as a way to find the proper weights and architecture of net that leads to minimum error between the desired (or predetermined) and predicted measures.

The comparison between process responses and the proposed model based on CCD matrix prediction has been shown in Fig. 10. Fig.11 shows the variation of mean squared error (MSE) during the training process of BPNN model. The performance of the proposed model has been illustrated in Fig.12.

4. Problem Definition

Obtaining the best set of A-GTAW process variables to simultaneously maximize DOP, minimize WBW and attain desired ASR, is the main objective of this study. Consequently, process output measures could be considered together to build a multiple process response in the optimization procedure. Thus, the optimal design could be formulated as a multi-response optimization problem illustrated as Eq. (7):

Maximum DOP = DOP (F, I, S) (7)

Minimum WBW = − WBW (F, I, S)

Desired AS= [1-1.4]

In this study achieving low WBW, high DOP and desired AR simultaneously required for multi-criteria optimization. Therefore, process multi-responses are changed into a single measure using Eq. (8), where w₁ and w₂ are weighting coefficients to show the importance of DOP and WBW respectively. Based on the literature survey which has been confirmed via experimental tests, in order to avoid solidification cracks the best interval for AR is [1.0-1.4] [20]. Solidification cracking tendency is significantly influenced by width to depth ratio (WBW to DOP (W/D), which can be minimized by ensuring that this ratio is between 1 and 1.4. (Fig. 13).

Minimize F (F, C, S) = (W₁×DOP) - (W₂×WBW), (1.0 < AR < 1.4) (8)

5. An Introduction To Heuristic Algorithms

Nowadays different heuristic algorithms for different optimization purposes have been proposed (including simulated annealing (SA), genetic (GA), Tabu search (TS), ant colony (AC), bee colony (BC), particle swarm optimization (PSO), and etc.,) among them PSO and SA, due to their advantages are mostly being employed. Easy programming (few input parameters to adjust) and fast convergence are the major merits of PSO algorithm. Whereas, in high dimensional space, falling into local optimum traps may be considered as a weakness for PSO algorithm. Based on the SA mechanism this algorithm could avoid getting trapped into local optimum which can be considered as a major excellence over other algorithms [19].

In this study, PSO and SA algorithms due to their mentioned merits, have been employed as the heuristic algorithms to optimize A-GTAW process variables in order to achieve maximum DOP, minimum WBW and proper value of ASR. In this study, PSO has been used twice (to determine the most appropriate architecture for BPNN and optimize the process measures). Next, SA algorithm has been used to evaluate the performance of PSO algorithm. Furthermore, a set of validation experiments has been conducted in order to confirm the proposed approach.

5.3. Simulated annealing algorithm

To interpolate between the process input variables intervals to select the most appropriate values of process input parameters reaching the desired output characteristics (e.g. minimum WBW and maximum DOP), different procedures have been introduced among which heuristic algorithms have been extensively employed for different optimization problems. All heuristic algorithms are reminiscent of biological or physical processes. In this regard, SA algorithm is reminiscent of annealing in heat treatment process [21, 22]. In annealing process, metals are heated up to a specific and pre-determined temperature (near the melting point), at which all metal particles are in random motion. Then, all metal particles rearranged by cooling down slowly toward the lowest energy state. As the cooling process is conducted appropriately slowly, lower and lower energy states are achieved until the lowest energy state is reached. Similarly, in A-TIG welding process the lowest energy level gives the optimized value for variables based on an energy function is created and minimized. The mechanism of SA algorithm is defined as follows [23]:

Defining an acceptable answer space and generating an initial random solution in this space. Next, the new solution’s objective function (C₁) is computed and compared with the current ones (C₀). A move to a new solution is made either the new solution has better value or the value of SA probability function (Eq. (9)) is higher than a randomly generated number between 0 and 1 [22]:

Where, temperature parameter is shown by T_k, which acts as the temperature in the physical annealing process does [21]. Eq. (10), is used as a temperature reduction rate to cool down the pre-determined temperature at each iteration.

Where, the current and former temperatures are shown by T_k+1 and T_k respectively. The cooling rate also presented by parameter α. Consequently, at the first iterations of SA due to higher temperature, most of the not improving (or even worsening) moves may be accepted. Nonetheless, as the algorithm proceeds and temperature is reduced only improving moves are likely to be accepted. This strategy could help the algorithm avoid being trapped in local minimum and jump out of it. After a specific number of iterations, a number of iterations in which no development is detected, and a pre-determined run time, the algorithm may be dismissed.

5.4. Particle swarm optimization (PSO) algorithm

PSO is a heuristic algorithm proposed by Kennedy and Eberhart [24]. It begins with a population of random solutions which is updated and searched for optimum ones. The current optimum particles are followed by the random solutions (known as particles) through the problem space. The problem space is connected with the best obtained solution and its corresponding location shown by “pBest” and “gBest” respectively. Each particle keeps track of the “pBest” and “gBest” in the problem space by changing its velocity towards them. The following Equations (11 and 12) used updating the particles [25–27].

V_i+1 = w × V_i + (C₁ × r_i × (pBest_i- X_i)) + (C₂ × r_i × (gBest_i- X_i)) (11)

X_i+1 = X_i + V_i+1 (12)

Where, (V_i+1) for each particle has been determined based on its previous velocity (V_i), global best solution (pBest) and location (gBest). Eq. (9) has been used for updating the particle’s position (X_i) [27]. The terms “r₁” and “r₂” are two random numbers generated independently in the range of [0, 1]. There are acceleration constants (“c_l” and“c₂”) using which pull each particle (solution) towards “pBest” and “gBest” positions. Inertia weight “w”, acts as an important parameter in PSO algorithm convergence behavior. In order to explore the answer space globally, the large amount of “w” required, while the small amounts explore nearby regions of the space [28].

Based on the literature survey, the architecture (number of hidden layers and nods in hidden layers) of BPNN in most studies has been determined using trial and error. Whereas, in this study PSO algorithm has been employed to determine the PBNN architecture. Furthermore, the optimization of the proposed BPNN models have been carried out using PSO algorithm. Moreover, SA algorithm has been used to confirm the performance of PSO algorithm (avoiding getting trapped in the local optima).

The performance of each evolutionary algorithm is affected by its own distinctive adjusting parameters. The details of the PSO performance are well documented in Refs [23–27].

The adjusting parameters used for controlling the SA and PSO algorithms are carried out as the following.

PSO variables: Population: 50; Learning factor c₁ and c₂: 2; Number of iteration performed: 30.

SA variables: Temperature reduction rate: 0.91; Processing time: 30; seconds Initial temperature: 700.

6. Results And Discussion

Different weights (W₁ and W₂) may have been considered for A-GTAW process responses (DOP and WBW) based on the importance considered. In this study the value of 0.5 has been considered for W₁ and W₂ for DOP and WBW. In this study optimization procedure has been used for two conditions. In the first condition the demotion of weld bead geometry has not been restricted. In the second condition the dimensional restriction has been imposed to the optimization procedure. In the second condition, the maximum value for DOP has been considered 5 mm. At the same token desired AR ([1.0-1.4]) has been taken into account as the second limitation. Figure 14, illustrates the cross section of weldment for optimization of the second condition. Based on the nature of the PSO algorithm, its convergence is faster than SA algorithm. Furthermore, as the PSO drawback is falling into optimum traps, its performance could be better to be checked by another algorithm. In this paper, the performance of PSO algorithm has been checked by SA algorithm. The convergence of PSO and SA algorithms has been shown by Fig. 15. Tables 5 and 6, represents the results of PSO and SA optimization for the both mentioned conditions. Based on the results, PSO and SA could accurately optimize the process responses (with less than 7% error).

Table 5

Optimal A-TIG welding process variables and coressponding process measures for CCD matrix
Output	Algorithm	Process variables				Predicted	Experimental	Error (%)
Output	Algorithm	F		S	C	Predicted	Experimental	Error (%)
W_DOP=0.50 and W_WBW=0.50		Considering weld bead geometry restriction
DOP	SA		60	190	129	4.96	5.11	3.0
DOP	PSO		71	190	128	4.95	5.07	2.4
WBW	SA		60	190	129	5.70	5.56	2.7
WBW	PSO		71	190	128	5.68	5.55	2.1
AR	SA		60	190	129	1.14	1.08	5.2
AR	PSO		71	190	128	1.14	1.09	5.1

Table 6

Optimal A-GTAW welding process variables and coressponding process measures for BBD matrix
Output	Algorithm	Process variables				Predicted	Experimental	Error (%)
Output	Algorithm	F		S	C	Predicted	Experimental	Error (%)
W_DOP=0.50 and W_WBW=0.50
DOP	SA		74	133	100	4.92	4.62	6.0
DOP	PSO		75	134	100	4.94	4.68	5.5
WBW	SA		74	133	100	5.61	5.36	4.3
WBW	PSO		75	134	100	5.62	5.40	4.0
ASR	SA		74	133	100	1.14	1.16	1.8
ASR	PSO		75	134	100	1.13	1.15	1.8

7. Conclusion

An important factor which affects the weldments’ quality in different welding processes is the proper selection of process variables levels. The modeling and optimization of A-TIG welding process for AISI316L austenite stainless steel parts considering both the process variables and percentage of activating fluxes combination has been addressed throughout this study. First, CCD based on RSM has been employed to determine the experimental design matrix required for data gathering, modeling and optimization purposes. Next, DOP and WBW values have been measured using MIP software. Based on the results of WBW and DOP, AR values have been computed. Then, BPNN has been employed to establish the relations between process input variables (welding speed, current and percentage of activating fluxes combination) and output responses (DOP, WBW and AR). Moreover, in order to determine the proper BPNN architecture, PSO algorithm has been used. Then, PSO algorithm has been used again to optimize the proposed proper BPNN model in such a way that DOP increased and WBW decreased simultaneously and achieved the desired AR. Furthermore, the PSO algorithm performance has been checked using SA algorithm. Using the proposed hybrid BPNN-PSO approach either process input variables have been optimized (190 mm/sec for welding speed and 128 Amp for welding current) and the optimum formula (71% SiO₂ and 29% TiO₂) for activating fluxes combination has been determined in order to achieve the desired process output measures (maximum DOP, minimum WBW and desired AR). The result of proposed optimization procedure showed that the proposed method can precisely simulate and optimize (with less than 7% error) the A-TIG welding process.

Nomenclature

Artificial neural network	ANN
Particle swarm optimization	PSO
Activated gas tangent arc welding	A-GTAW
Gas tangent arc welding	GTAW
Design of experiments	DOE
Box-behnken design	BBD
Central composite design	CCD
Weld bead width	WBW
Welding current	I
Welding speed	S
Back propagation neural network	BPNN
Microstructural image processing	MIP
Multi-layer perceptron	MLP
Mean squared error	MSE
New solution	C₁
Current solution	C₀
Current temperatures	T_k+1
Former temperatures	T_k
Cooling rate	α
Velocity	V_j
Position	X_j
Random numbers	r₁ and r₂
Acceleration parameters	c₁ and c₂
Inertia weight	γ
Best position of particle	p_j
Best position of group	p_g
Particle	j^th
Current velocity	V_j+1
Former velocity	V_j
Particle’s position	X_i
Global best location	gBest
Current best location	pBest
Inertia weight	w

Declarations

Acknowledgments

We are thankful to the editor and reviewer of this journal for suggesting the valuable improvements and allowing appropriate time for updating the manuscript.

Conflicts of interest

The authors whose names are listed immediately below certify that they have NO afﬁliations with or involvement in any organization or entity with any ﬁnancial interest (such as honoraria; educational grants; participation in speakers’ bureaus; membership, employment, consultancies, stock ownership, or other equity interest; and expert testimony or patent-licensing arrangements), or non-ﬁnancial interest (such as personal or professional relationships, afﬁliations, knowledge or beliefs) in the subject matter or materials discussed in this manuscript.

Funding

Not applicable' for this section

Availability of data and material

The data and material could be available if is required

Code availability

The Code could be available if is required

Ethics approval

The manuscript will not be submitted elsewhere until the editorial process is completed.

Consent for publication

The Authors grant the Publisher the sole and exclusive license of the full copyright in the Contribution, which license the Publisher hereby accepts. Consequently, the Publisher shall have the exclusive right throughout the world to publish and sell the Contribution in all languages, in whole or in part, including, without limitation, any abridgement and substantial part thereof, in book form and in any other form including, without limitation, mechanical, digital, electronic and visual reproduction, electronic storage and retrieval systems, including internet and intranet delivery and all other forms of electronic publication now known or hereinafter invented.

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Azadi Moghaddam M, Golmezergi R, Kolahan F, “Multi-variable measurements and optimization of GMAW parameters for API-X42 steel alloy using a hybrid BPNN–PSO approach”, Measurement, 2016; 92: 279–287.