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Demands for improved productivity, efficiency, and quality pose challenges to the welding industry. In submerged arc welding (SAW) process, the weld quality is not only closely related to the geometry of weld bead but it is also, greatly affected by welding input parameters, a relationship which is complicated because of the nonlinear nature of the welding processes. Nowadays, trialanderror and statistical methods to determine optimal conditions incur considerable time and cost. In order to overcome these problems, a couple of nontraditional methods have been reported. This paper reports the applicability of fuzzy logic (FL) to predict the weld penetration in SAW process as affected by welding input parameters. FL is a computer technique which allows expressing, evaluating, and simplifying complexities in regard with the relationships in a process by describing the dependencies between outputs and input parameters in a linguistic form. For developing the fuzzy logic model, the arc voltage, welding current, welding speed, electrode stickout, and weight percentage of TiO_{2} / Cr_{2}O_{3} nanoparticles coated on mild steel plates before actual welding operation, were taken as the input parameters and the weld penetration as the response. In order to generating experimental data, a fivelevel fivefactor central composite rotatable design (CCRD) of experiments was employed. Beadonplate welds were placed on mild steel plates using automatic SAW machine. Data were collected and FL modeling was carried out to establish input–output relationships of the process. The values obtained from this technique was compared with experimental results and presented in graphical forms.
TiO_{2}/Cr_{2}O_{3} nanoparticles, weld penetration, submerged arc welding, fuzzy logic, central composite rotatable design
Demands for improved productivity, efficiency, and quality pose challenges to the welding industry. As materials become ever more sophisticated in their chemical composition to provide everbetter functionally specific properties, a more complete and precise understanding of how such materials can be joined for optimal effectiveness and efficiency will become essential.
One of the most widely used welding methods in industries and research organizations is the SAW. SAW is a high quality welding process commonly used for fabricating large diameter line pipes, pressure vessels and wind turbine towers due to its high deposition rate, ease of automation and low operator skill requirement. In order to achieve high melting efficiency required for high productivity, best weld quality and good mechanical properties in manufacturing industries, the welding process parameters need to be optimized. During SAW process, operator cannot observe the weld pool and cannot directly interfere with the welding process. To consistently produce high quality of welds, SAW requires skilled welding personnel with significant experience and a proper selection of welding parameters for a given task. Many attempts have been made by researchers to establish the SAW process for a desired weld quality. Traditionally the desired welding parameters are obtained either from experience, charts or handbooks which are difficult, cumbersome and they do not ensure that the chosen welding parameters are optimal for the particular environment. In recent years, mathematical models have been developed to correlate the welding performance such as weld bead width, shape and size [1–5] with welding parameters. Multiple regression techniques have been used to establish mathematical models for the weld bead geometry [67]. One of the weld quality characteristics extremely important for structural integrity is the weld bead geometry. One of the important dimensions in weld bead geometry is the weld penetration which is defined as the depth to which the molten metal penetrates into a weld, determines the size and stress carrying capacity of weld beads that hold the joints together [8].
Due to the inadequacy and inefficiency of the regression models to explain the nonlinearity and other complexities existing in manufacturing processes between the responses and input parameters, the usage of artificial intelligence techniques in modeling of welding operations is getting more and more inescapable. These techniques can be considered as a branch of computer science and try to bridge the gap between humans and machines by giving the machines some aspects of human capabilities. One type of intelligent system that has found popularity recently is FL. FL is well suited for modeling complex and uncertain problems that can be controlled by humans. Several authors have performed the application of fuzzy methodology to estimate welding quality in different welding processes [9–13]. FL due to its capability in approximating the nonlinear functions and incorporating the human knowledge has been widely used to solve many engineering problems [14]. FL is a mathematical theory of inexact reasoning that allows us to model the reasoning process of humans in linguistic terms and is very suitable in defining the relationship between the system inputs and the desired system outputs [15].
It has been reported that active fluxes such as TiO_{2} and Cr_{2}O_{3} when added to weld puddle, can modify fusion zone geometry dramatically in GTA welding [16]. On the other hand, it has been reported that addition of oxide nanoparticles to the weld puddle can modify the fusion zone geometry in SAW process and have a significant role on improving the hardness [11]. What is then missing is the application of TiO_{2, }Cr_{2}O_{3} and nanoparticles in welding processes in general. Nanomaterials are defined as particles having diameters ranging from 1 nm to 100 nm [17]. Their small size and large surface and volume effects offer unique mechanical, electrical, magnetic, optical, and physiochemical properties which make them suitable candidates for different applications in defense, electronic, aerospace, and chemical industries [18]. In recent years, a great deal of attention has been given to the application of nanomaterials in welding research [9, 19–21] but the fact is that scientific investigations into the role of nanomaterials in welding processes will still remain to be seen in the future.
Since it was not possible to mix up the TiO_{2} and Cr_{2}O_{3} nano particle with the flux due to its nano size therefore, it was decided to disperse them in ethanol and then apply the obtained paste on the low carbon plates in different weight percent as per the design matrix before welding operation.
2.1. Design of experiments
Table 1. The input parameters and their ranges
Notation 
Parameter 
Units 
Code values 

2 
1 
0 
+1 
+2 

I 
Welding current 
Amp 
500 
550 
600 
650 
700 

V 
Arc voltage 
Volts 
24 
26 
28 
30 
32 

N 
Electrode stickout 
mm 
30 
32.5 
35 
37.5 
40 

S 
Welding speed 
mm/min 
300 
350 
400 
450 
500 

F 
NanoParticles 
TiO_{2} 
Wt.% 
10 
30 
50 
70 
90 
Cr_{2}O_{3} 
90 
70 
50 
30 
10 
Table 2. Design matrix
No 
V 
I 
S 
N 
F 
P 
1 
1 
1 
1 
1 
1 
9.263 
2 
1 
1 
1 
1 
1 
5.951 
3 
0 
0 
0 
0 
0 
8.027 
4 
0 
0 
0 
0 
2 
5.982 
5 
1 
1 
1 
1 
1 
10.005 
6 
1 
1 
1 
1 
1 
7.746 
7 
1 
1 
1 
1 
1 
6.442 
8 
0 
2 
0 
0 
0 
7.171 
9 
0 
0 
0 
2 
0 
7.697 
10 
1 
1 
1 
1 
1 
10.738 
11 
2 
0 
0 
0 
0 
3.896 
12 
2 
0 
0 
0 
0 
10.245 
13 
1 
1 
1 
1 
1 
5.951 
14 
0 
0 
0 
0 
0 
8.027 
15 
0 
2 
0 
0 
0 
8.178 
16 
0 
0 
0 
2 
0 
7.610 
17 
0 
0 
0 
0 
0 
8.027 
18 
1 
1 
1 
1 
1 
4.938 
19 
1 
1 
1 
1 
1 
6.901 
20 
1 
1 
1 
1 
1 
6.466 
21 
1 
1 
1 
1 
1 
9.748 
22 
0 
0 
0 
0 
0 
8.027 
23 
1 
1 
1 
1 
1 
6.663 
24 
0 
0 
0 
0 
2 
8.338 
25 
0 
0 
0 
0 
0 
8.027 
26 
1 
1 
1 
1 
1 
8.716 
27 
1 
1 
1 
1 
1 
7.117 
28 
1 
1 
1 
1 
1 
10.063 
29 
0 
0 
2 
0 
0 
8.439 
30 
0 
0 
2 
0 
0 
6.380 
31 
1 
1 
1 
1 
1 
6.209 
32 
0 
0 
0 
0 
0 
8.027 
RSM provides a powerful means to achieve breakthrough improvements in product quality and process efficiency. From the viewpoint of manufacturing fields, this can reduce the number of required experiments when taking into account the numerous factors affecting the experimental results. RSM can show how to conduct the fewest number of experiments while maintaining the most important information [22]. The experiments for the present work have been carried out using fivelevel CCRD [22]. In this investigation, the number of input parameters considered for the response surface modeling is five, and the number of experiments conducted is thirty two. The alpha value selected as per central composite design is 2.0. The independently controllable process parameters identified for the experimentation are: arc voltage (V), welding current (I), welding speed (S), electrode stickout (C), and weight percent of TiO_{2}/Cr_{2}O_{3} and the response, is the weld penetration (P). The working level for each input parameter was determined by doing one factor at a time welding technique and inspecting the weldments for absence of visible defects and good appearance. The coded value is calculated from the following relationship:
$X_{i}=\frac{2\left[2 \mathrm{X}\left(\mathrm{X}_{\mathrm{max}}+\mathrm{X}_{\mathrm{min}}\right)\right]}{\left(\mathrm{x}_{\mathrm{max}}\mathrm{x}_{\mathrm{min}}\right)}$ (1)
where X_{i} is the required coded value of a parameter X. X is any value of the parameter from X_{min} to X_{max}, X_{min }and X_{max} are the lower level and the upper level of the parameter respectively. The selected input parameters, their notations, and their limits are given in Table 1. The design matrix for all the 32 experiments is listed in Table 2.
2.2 Nanoparticles
2.2.1 TiO_{2}
(AEROXIDE TiO_{2 }P 25) is a highly dispersed titanium dioxide manufactured according to the AEROSIL process, obtained from the Degussa AG, Germany. Titanium Dioxide P 25 has an average primary particle size of about 21 nm and a specific surface of about 50 m^{2}/g.
2.2.2 Cr_{2}O_{3}
A simple synthesizing procedure was used to produce Cr_{2}O_{3} nanoparticles. In this procedure, some amount of ammonium dichromate (NH_{4})_{2}Cr_{2}O_{7} was placed in a crucible, and then by approaching a flame, it was ignited. Subsequently, its color changed to green and Cr_{2}O_{3} powder was produced. In this reaction, the combustion liberated N_{2} gas that affected the formation of Cr_{2}O_{3} nano particles by obstructing the growth of particle sizes. Characterization of the Cr_{2}O_{3} nanoparticles and its grain size, was obtained by using XRD and SEM. The properties of Cr_{2}O_{3} nanoparticles are given in Table 3.
Table 3. Properties of Cr_{2}O_{3} nanoparticles
Name 
Formula 
Crystal system 
Particle size 
Density 
Chromium Oxide 
Cr_{2}O_{3} 
Rhombohedral 
68.568 nm 
5.345 g/cm³ 
Figure 1. XRD of Cr_{2}O_{3} nanoparticles
Figure 2. SEM of Cr_{2}O_{3} nanoparticles
2.3 Conducting the experiment as per the design matrix
The experiments were conducted at the Welding Research Center of Razi University with the following details:
Thirty two specimens were prepared and their surfaces were thoroughly cleaned and the paste of TiO_{2}/Cr_{2}O_{3} nanoparticles according to Table 1, was coated on each plate as per the design matrix and welding was carried out at random order. Subsequent to welding, two transverse specimens were cut from each welded plate at mid length and were prepared by the usual metallurgical polishing methods and etched with 2% nital. The profiles of the weld penetration were traced by using Olympus optical microscope. The chemical composition of base plate is given in Table 4. The experimental setup and the schematic illustration of weld penetration are shown in Fig. 3 and Fig. 4, respectively.
Table 4. Chemical composition of base metal
Element 
Cr 
P 
S 
Si 
Ti 
Mn 
C 
Fe 
Wt% 
0.031 
0.007 
0.01 
0.024 
0.002 
0.417 
0.113 
Balance 
Figure 3. The experimental setup
Figure 4. Weld penetration
3.1 Computational intelligence model
Figure 5. Model representation of the weld penetration using fuzzy logic
Fuzzy logic is a popular soft computing methodology Among various methods that are available. it is found effective and applied by many researchers for modeling and optimization.Fuzzy logic technique based on fuzzy set theory was first introduced by Lotfi Zadeh [23] and it is used as a tool for computing with language. Since then the number and variety of applications of fuzzy set theory in engineering field have grown significantly in the recent years including the area of artificial intelligence (AI). Here, in order to predicting the combined effect of coating flux and aforesaid welding parameters mentioned above on the weld bead penetration during the SAW of mild steel plates, a fuzzy model as shown in Fig.5 is used. In this study, the weld penetration, is adopted as a function of the five input parameters namely the arc voltage (V), welding current (I), welding speed (S), electrode stickout (N) and coated flux (F).
3.2. Fuzzy logic
Fuzzy logic approach uses a fuzzy set that allows an infinite number of intervals between true and false. This means that there will be other stages besides true and false, [25]. Fuzzy approach encompasses fuzzy set theory, fuzzy logic and fuzzy measure theory. Many engineering fields have already benefited from the new methodological possibilities presented by fuzzy concepts. Fuzzy logic is based on imprecision and non numerical information, fuzzy logic mimics the way human make decisions using linguistic reasoning [25]. Fuzzy systems base their decisions on inputs and outputs in the form of linguistics variables. The variables are tested with IFTHEN rules, which produce one or more responses depending on which rules are asserted. Generally, the system inputs are passed to a process called fuzzification. In the fuzzification process, the input data will undergo some translation into linguistic quantity such as Low, Medium, High. The translated data will be sent to an inference mechanism that will apply the predefined rules. The inference mechanism will generate the output in linguistic form. The linguisticoutput will go through defuzzification process, [24]. The output will then turn out to be in numerical normal data form. In fuzzy inference engine, the truth value for the premise of each rule is computed and applied to the conclusion part of each rule. The response of each rule is weighed according to the degree of membership of its inputs and the centroid of the response is calculated to generate the appropriate output. There are a lot of different shapes of fuzzy set. Some of the common shapes are Pi curve, beta curve, Gaussian curve and triangle. Triangle is the most preferred fuzzy shape as it can be easily represented with a minimum of computing power. A set of fuzzy rules has to be developed by a fuzzy designer. A more complicated system will have more complex rules. The defuzzification process is defined as the conversion of a fuzzy quantity, represented by a membership function, to a precise or crisp quantity. There are two commonly used techniques for the defuzzification of fuzzy quantities [25]. They include the Max method and Centroid method. The fuzzy algorithm allows here building a nonlinear functional relationship between the input variables and the output. The membership functions and the rule base are defined to best represent the experimental results. In the present study, Isosceles triangles are used to represent the membership shape with a fixed base length. The membership functions are defined by the following general equation:
triangle $(x ; a, b, c)=\left\{\begin{array}{cc}{0} & {x \leqslant a} \\ {\frac{xa}{ba}} & {a \leqslant x \leqslant b} \\ {\frac{cx}{cb}} & {b \leqslant x \leqslant c} \\ {0} & {c \leqslant x}\end{array}\right.$ (2)
where a, b, c stand for the triangular fuzzy triplet which determine the x coordinates of the three corners of the underlying triangular membership function as shown in Fig(6).
Figure 6. Triangular membership function
3.3 Fuzzy logic modeling
The optimum structure of the fuzzy model which is employed in this paper is described in Table 5. In order to performing FL, symmetric triangular membership functions for the input and output parameters are defined.
Table 5. Selected structure of the proposed fuzzy model
Type of fuzzy inference system (FIS) 
Mamdani 
Inputs / Output 
5/1 
Input membership function types 
Triangular 
Output membership function types 
Triangular 
Number of input membership functions 
5/5/5/5/5 
Number of output membership function 
100 
Rules weight 
1 
Number of fuzzy rules 
27 
And method 
Min 
Implication method 
Min 
Aggregation method 
Max 
Defuzzification method 
Centroid 
Figure 7. The membership functions of the inputs and output parameters
Figure 8. Comparison between the experimental and predicted values of the weld bead penetration using the fuzzy logic model
Figure 9. Fuzzy predicted weld penetration as a function of the input parameters
Table 6. Some of the rules involved in the fuzzy logic model
No 
Rules 
1 
If (V is mf2) and (I is mf4) and (S is mf3) and (N is mf2) and (F is mf2) then (P is mf79) 
2 
If (V is mf4) and (I is mf2) and (S is mf4) and (N is mf4) and (F is mf2) then (P is mf31) 
3 
If (V is mf3) and (I is mf5) and (S is mf3) and (N is mf3) and (F is mf3) then (P is mf93) 
4 
If (V is mf3) and (I is mf3) and (S is mf5) and (N is mf3) and (F is mf3) then (P is mf55) 
5 
If (V is mf5) and (I is mf3) and (S is mf3) and (N is mf3) and (F is mf3) then (P is mf63) 
Here, five symmetric triangles are used for building up the input membership functions. Where, the peak of each triangle indicates the main values in experiments. For establishing the output membership functions, one hundreds symmetrical triangular membership functions are used in the range of zero to 100, where 0,1,…, 99 indicate the locations of triangle peaks. Subsequently, the range of zero to 99 is marked as 3.896 mm to 10.738 mm, respectively. By doing this sort of replacements we, therefore, obtained one hundred symmetrical triangular membership functions for the weld penetration. Fig. 7ae depict the membership functions for the input parameters. In addition, the membership functions of the output parameter are shown in Fig. 7f. Some parts of twenty seven rules, which are chosen for the fuzzy logic model, are shown in Table 6.
The results of the proposed fuzzy model are shown in Fig. 8 and Table 7, in which, the mean relative error (MRE) is defined by:
$M R E=\frac{1}{N} \times \sum_{i=1}^{N}\left\frac{P_{\text { exp }}P_{\text {pred}}}{P_{\text { exp }}}\right$ (6)
where P_{exp }and P_{pred} are the experimental and predicted values of the weld penetration, respectively and N is the number of welding runs. According to the obtained results, it is to be concluded that the predictions made by fuzzy model are in excellent agreement with the experimental data.
Table 7. Comparison between the experimental and predicted values of the weld penetration using the fuzzy logic model
No 
Experimentally measured penetration, P_{exp} 
Fuzzy predicted penetration, P_{pred} 
MRE% 
1 
9.263 
9.28 
0.184 
2 
5.951 
5.96 
0.151 
3,14,17,22,25,32^{a} 
8.027 
8.03 
0.037 
4 
5.982 
5.96 
0.368 
5 
10.005 
10.0 
0.050 
6 
7.746 
7.69 
0.723 
7 
6.442 
6.43 
0.186 
8 
7.171 
7.20 
0.404 
9 
7.697 
7.69 
0.091 
10 
10.738 
10.7 
0.354 
11 
3.896 
3.90 
0.103 
12 
10.245 
10.3 
0.537 
13 
5.951 
5.96 
0.151 
15 
8.178 
8.18 
0.024 
16 
7.61 
7.63 
0.262 
18 
4.938 
4.95 
0.243 
19 
6.901 
6.89 
0.159 
20 
6.466 
6.43 
0.557 
21 
9.748 
9.76 
0.123 
23 
6.663 
6.66 
0.045 
24 
8.338 
8.34 
0.024 
26 
8.716 
8.74 
0.275 
27 
7.117 
7.13 
0.183 
28 
10.063 
10.1 
0.368 
29 
8.439 
8.46 
0.249 
30 
6.381 
6.38 
0.002 
31 
6.209 
6.18 
0.467 
Accuracy of the FL model in actual welding conditions was obtained by conducting conformation tests. This was done by assigning different values to different input parameters within the working levels but different from those already present in the design matrix. For this purpose, five welding runs were performed and their penetrations were measured. The percentage of error provided the deviation of predicted values from the actual measured values. It is found from Table 8 that the average error for the model is 1.43%.
Table 8. Comparison of the experimental and predicted values of the weld penetration
S. no. 
Process variables in coded form 

Predicted values 
Experimental values 
%Error 

V 
I 
S 
N 
F 
P (mm) 
P (mm) 
P (mm) 

1 
1 
0 
0 
0 
0 

7.32 
7.15 
2.37% 
2 
0 
0 
0 
1 
0 

8.45 
8.33 
1.44% 
3 
0 
1 
0 
0 
0 

9.41 
9.24 
1.84% 
4 
0 
0 
1 
0 
0 

7.69 
6.74 
0.64% 
5 
0 
0 
0 
0 
1 

8.04 
8.11 
0.86% 
Average error % 




1.43% 
The effects of the five input parameters on the weld penetration based on the fuzzy logic predictions are shown graphically in Fig. 9ae.
As shown in Fig. 9a the weld penetration increases slightly with the increase in the arc voltage. This could be attributed to the slight increase in the heat input into the workpiece. However, quantitatively the effect is not very much. Many investigators [26] reported that arc voltage in a consumable electrode process has no significant effect on the weld penetration.
From Fig. 9b, it is observed that penetration increases with the increase in welding current. Basically, the increase in current gives rise to the increase in heat input into the weld bead causing greater volume of the base plate to melt and hence, achieving deeper penetration. Furthermore, the increase in welding current increases the temperature and the heat content of the droplets, resulting in more heat being transferred to the base metal. In addition, increase in the welding current also increases the momentum of the filler metal droplets striking the weld pool and results in a deeper penetration [2728].
Fig. 9c shows that the welding speed has no significant effect on weld penetration. As shown in Fig. 9d, the weld penetration decreases with the increase in electrode stickout because increase in the electrode stickout increased the circuit resistance, which reduced the welding current. This decrease in the welding current reduced the heat input and hence reduced the penetration.
Fig. 9e shows that the weld penetration increases with the increase in weight percentage of the TiO_{2} nanoparticles pasted on the mild steel plates. Welding pool penetration can be improved significantly by preplacing a thin layer of coated flux of nanooxides on the surface of substrate. Weld penetration can also be determined by the fluid flow mode in the weld pool, which is driven by the electromagnetic force, surface tension gradient and buoyancy force. Among them, the surface tension gradient on the welding pool is the principle variable that changes the convection mode. Generally, the surface tension decreases with the increasing temperature, ∂σ /∂T < 0, for pure metal and many alloys. In the weld pool for such materials, the surface tension is higher in the relatively cooler part of the pool edge than that in the pool center under the arc, and hence the fluid flows from the pool center to the edge. Surfacetensiondriven convection is also called Marangoni convection. The heat flux is easily transferred to edge and the weld pool shape is relatively wide and narrow as shown in Fig. 10a [29]. Heiple and Roper proposed that surface active elements such as oxygen, sulfur and selenium can change the temperature coefficient of the surface tension for steels from negative to positive, ∂σ /∂T > 0, and further changes the direction of the fluid flow in the weld pool as illustrated in Fig. 10b [29]. In that case, a relatively deep weld was produced.
Figure 10. Marangoni convection mode by surface tension gradient in welding pool [16]
In our experiments, the oxygen in the weld from decomposition of the coated nanooxide flux (TiO_{2} and Cr_{2}O_{3}) played the important role as an active element and changed the Marangoni convection mode of the liquid weld pool. As the oxygen content in the weld increased, the Marangoni convection mode changed from outward to inward first, and then the inward convection becomes weaker or changed to the outward direction as the oxygen content increases in the weld [16] the Cr_{2}O_{3} oxide is less stable than TiO_{2} and more easily decomposed under the arc. The decomposed oxygen would dissolve in the weld pool and quickly increase the oxygen content in the weld. If the oxygen content is too high, the inward Marangoni convection becomes weak or changes to the outward direction and the weld pool penetration decreases again. However, the TiO_{2} oxide is more stable and not decomposed completely under the arc, which caused the oxygen content in the weld pool to be relatively low and the Marangoni convection mode is maintained in the inward direction [16].
In this paper, a fuzzy logic model is developed to predicting the weld penetration in submerged arc welding process. The model was designed to take into account the effect of the arc voltage (V), welding current (I), welding speed (S), electrode stickout (N), coated flux (F). A model based on twenty seven fuzzy rules was able to reflect the effect of these input parameters, and resulted in a low estimation error.
The important parameters, which significantly affect the weld penetration, have also been identified by this technique. Within limitations of the present work, the following conclusions are summarized as follow:
1. Out of the five input parameters considered, welding current had a significant positive effect whereas, the welding speed had no significant effect on the weld penetration.
2. Arc voltage had a slightly positive effect on the weld penetration.
3. The electrode stickout had a negative effect on the weld penetration.
4. Increasing weight percent increasing of TiO_{2} nano particle had a positive effect on the weld penetration.
Based on the obtained results, it is concluded that the fuzzy logic is a reliable technique to predicting the weld penetration in SAW process due to its low error rate as indicated in the study.
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