1 Introduction

Technology advancement in today’s fast-paced world compels nearly all factories and engineering companies to produce long-lasting, high-quality goods at competitive prices. While many products are created independently as standalone pieces, they often need to be put together in order to function in their intended real-world contexts [1,2,3,4]. Welding is the method of choice in several sectors (including the automotive, aviation, hydrocarbon, pharmaceutical, power, and agricultural industries) for joining thick and thin, and often incompatible materials to easily produce efficient, durable, and cost-effective products [5,6,7,8]. Welding saves time and money when compared to other methods like adhesive bonding and mechanical fastening of joining materials. It creates a weld so strong and durable that it’s nearly impossible to detach the joined pieces. The American Welding Society (AWS) recognizes 94 distinct welding methods, one of which is gas metal arc welding (GMAW) [9,10,11].

GMAW has been employed in a broad range of industries since its commercialization in the late 1950s, including shipyards, gasoline and oil pipelines, pressure vessels, boiler pipes, heat exchangers, coal conversion, and chemical parts. There are three ways in which metal can be transferred: globular arc transfer, spray arc transfer, and shortcircuiting arc transfer. Out of these three modes of metal transfer, the shortcircuiting mode of metal transfer is quite popular due to its attributes like versatility in welding metals of different thicknesses and out-of-position welding capability. Although the short-circuiting method of metal transfer has its benefits, it also has certain downsides. In turn, it produces localized arc heat, which slows down the pace of the deposition process. When welding thick plates (6.35 mm or higher), cold lapping or a lack of fusion might develop if the best procedure is not used. When the machinery isn’t optimized properly, excessive spatter results from incorrect short-circuiting, which causes the unit to overheat [12,13,14].

To address the aforementioned issues, Miller Electric Mfg. LLC developed a revolutionary welding approach that improves on the conventional shortcircuiting mode of the GMAW technique. The manufacturer named this novel technique “regulated metal deposition” (RMD) due to its nature of controlling and adjusting the welding arc precisely with respect to the base material [15,16,17]. The company claims that this advanced method employs a sophisticated welding current waveform to control the short circuit. The thickness and constitution of the metal being joined are two factors that frequently affect waveform. As may be seen in Fig. 1, it can be broken down into seven separate stages. Each of these seven stages contributes to a larger cycle known as the RMD cycle [18]. Detailed explanations of the RMD cycle’s individual stages can be found in Fig. 2.

Fig. 1
figure 1

Different stages of metal transfer in the RMD process [18]

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The “ball” stage of an RMD cycle is characterized by a spike in current that melts the electrode head and results in a short circuit. The current drops off during the subsequent “background” stage, permitting the short circuit to take place. The “pre-short” stage then follows, during which the current is lowered to a safe level to shield the steady weld puddle from the arc force. When the molten head is in contact with the base metal at a lower current, this is known as the “wet” stage. The “pinch” stage involves a quick rise in current at the electrode head, producing the “pinch effect,” and resulting in a short circuit. The pinch effect is observed during the transitional period between the “pinch” and “clear” stages. As the “clear” stage concludes, the molten head separates from the electrode. The “blink” stage, in which short circuits are broken and the current significantly declines, closes the circuit and ends the cycle [19,20,21].

Fig. 2
figure 2

The RMD cycle

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Numerous scholars have suggested using GMAW and/or GTAW methods for welding low-alloy steel. Nevertheless, there are constraints inherent to these methods. On one side, GMAW is fast but unable to produce spatter-free and slag-free welds; on the other hand, GTAW produces spatter-free and slag-free welds but has the limitation of slow welding speed. Therefore, these conventional welding approaches are not financially sustainable in the current production context. This means that improvements in welding technology are essential. Take a look at the characteristics of RMD welding (in Table 1), which is as quick as GMAW and creates spatter- and slag-free welds like GTAW [22,23,24].

Table 1 Comparative advantages of the RMD technique over conventional arc welding processes
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Quality is a top priority in today’s production perspective. Quality is the extent to which a product satisfies its intended consumer. The product’s quality is determined by how well it meets the needs of its intended purpose in a variety of contexts [25,26,27]. Weld quality in the welding industry is primarily determined by the mechanical behavior of the weldments, which are in turn controlled by their chemical and metallurgical compositions. Weld bead geometry (WBG), which is closely connected to welding variables, also affects the mechanical-metallurgical aspects of the weldment. To summarize, welding variables determine weld quality. In the metalworking industry, arc welding techniques are widely recognized as among the most versatile and effective. A complicated interaction between a number of process variables affects the weld chemistry, mechanical characteristics, and metallurgical aspects of the weld joint, as well as the WBG. As a result, it is important to identify the best welding process conditions for achieving the specified weld quality. On the other hand, the optimization should be carried out in such a manner that all objectives are met concurrently. This type of optimization approach is known as multi-response optimization [28,29,30,31,32,33].

According to the available publications, several researchers have spent time perfecting techniques for modeling, simulating, and optimizing traditional arc welding procedures. To determine welding variables resulting in an ideal approach, a comprehensive study has been performed to identify correlations between welding variables, WBG, weld quality, and productivity [34,35,36,37]. WBG during electric arc welding was studied by Mistry [38], who looked at how different welding factors impacted the process. The effects of the input factors V, A, WS, and base metal-electrode tip distance on the resulting BW, DOP, and BH were analyzed. The research recommends using full penetration for the most robust and cost-effective welds. Furthermore, the research suggests that currently has a significant impact on penetration whereas voltage affects BW. RMD welding on low-carbon steel pipes was carried out by Costa and Vilarinho [39]. Tests have been conducted while the input variables of wire feed speed (WFS), WS, trim (TM), arc control, and weaving are all considered. No intrinsic defects like porosity, absence of fusion, or cracking were found during analysis. After conducting a macroscopic analysis of the specimens, it was discovered that raising the WFS led to an improvement in penetration and root reinforcement (RR) and a drop in face reinforcement (RF). The TM has also been the subject of research. WBG grows in tandem with the TM. This results in a reduction of RF. This study by Nouri et al. [40] analyzed the effect of pulsed-GMAW factors on the WBG. WS, WFS, vertical angle, and nozzle-to-workpiece distance were selected as the main factors. The degree to which they had an effect was determined by analyzing the WBG produced. Improvements in WFS are associated with improvements in BH, BW, and DOP, whereas decreases in these responses are seen with increments in WS. GMAW and RMD welding were used by Das et al. [41] to join 10 mm thick 2.25 Cr-1.0 Mo grade steel. Electrodes made of metal-cored wire were utilized as the filler. Samples were heat-treated after welding so that any resulting microstructural changes could be studied. The welded joints were also put through mechanical testing, with favorable findings. Joints with a root misalignment (High/Low) of 1.5 mm can be produced using either traditional or enhanced short-circuit GMAW procedures, as determined by a comparison of both techniques by Vilarinho and Nascimento [16]. Although updated GMAW welding procedures produced more durable components, traditional welding techniques produced weaker welds. To predict the WBG while accumulating 316 L stainless steel onto structural steel IS2062, Murugan et al. [42] created mathematical equations employing a five-level factorial method. OCV, WFS, WS, and nozzle-to-plate distance have all been studied for their effects on the responses of dilution, reinforcement, penetration, and width. The accuracy and practicality of the proposed modeling techniques have been verified. In order to aid in the choosing of process variables to obtain the required level of the overlay, graphical representations of the primary and interaction impacts of the control variables on dilution and WBG have been shown. Submerged arc welding (SAW) was performed on high-strength low-alloy steel by Sharma et al. [43] to examine the impact of various input variables on the final WBG. The WBG during cooling was observed as a function of the input factors of heat input and preheat temperatures. To demonstrate the relationship between preheating temperature and cooling time, a mathematical model was developed using the response surface method. Artificial neural networks (ANN) and genetic algorithms (GA) were utilized by Nagesh and Dutta [43] to investigate the WBG and provide the optimal result for GTAW. The “multiple layer regression” technique was utilized to create mathematical models, which took into account both the impacts of the input variables and the two-factor interactions. The effect of SAW elements on WBG was studied by Choudhary et al. [44]. Welding current, OCV and nozzle-to-plate distance were the input factors. BW, reinforcement, and penetration were the process’s results. In the investigation, it was shown that a higher current resulted in more reinforcement and penetration. To optimize the voltage, current, welding speed, and arc length in arc welding for rail car bracket assembly, Daniyan et al. [44] used the Taguchi approach and response surface methods (RSM). Taguchi analysis was used to assess how well the process performed in terms of hardness and distortion, and RSM was employed to analyze how the various input components interacted with one another. The researchers also published the results of an analysis of variance (ANOVA) and a regression analysis of the empirical study in order to assess the efficacy of the suggested model. Additional notable applications of optimization approaches in welding have been described by Vora et al. [45]. Datta et al. [46]. Dhas and Dhas [47], Karpagaraj et al. [48]. Benyounis and Olabi [49], and Chen et al. [50]. , .

Based on the research published so far, it is evident that a lot of effort has been put into assessing the HAZ, DOP, and BW properties of conventional arc welding methods. Welding factors such as V, A, GFR, etc. have been optimized using a variety of methods throughout the process. Researchers haven’t even tried much with more sophisticated GMAW methods like RMD welding. Machine specifications and the RMD process’s applicability are the sole topics covered in the manufacturer’s literature. However, no experimental evidence is discussed. As a result, there is a dearth of cutting-edge information about RMD welding. Therefore, the purpose of this research is to evaluate the WBG of low alloy steel and provide a novel optimization approach by employing utility function and TOPSIS approaches, both of which are important additions to the existing academic database covering this cutting-edge welding technique.

2 Materials and methods

RMD bead-on-plate (BOP) welding was carried out on a Cr-Mo Gr. 11 Cl. 2 (500 mm x 150 mm x 06 mm) steel plate with the assistance of semi-automatic welding equipment (Miller’s continuous 500). In everyday conversation, chromium-molybdenum steel is referred to as 1 ¼ chrome, although its official designation in the industry is either ASME SA387 or ASTM A387. Cr-Mo Gr. 11 Cl. 2 is applicable in many industries and general purposes such as the oil & gas industry, petrochemical industry, boilers & heat exchangers, shipping, automobile ancillaries, steel plants; cement industry, sugar industry, nuclear & aerospace pants, centrifugal industry, steel plants, port building, wastewater management, paper & pulp industry, and infrastructure building. It is useful in raising temperatures because it can handle high temperatures. It has higher flexibility, durability, longevity, good dimensional accuracy, weldability, excellent surface finishing, higher tensile strength, sturdiness, and can withstand heavy loads. These plates can entirely stress cracking corrosion resistance, crevice corrosion resistance, and pitting resistance [45,46,47].

The choice of consumables like filler material has a significant impact on both efficient and cost-effective manufacturing and the emission of harmful gases throughout the process. As filler materials, fabricators typically employ solid filler wire (SFW), flux-cored filler wire (FCFW), and metal-cored filler wire (MCFW) during arc welding operations. The MCFWs are the most recent addition to the welding world and offer the most advantages in terms of performance, profitability, and sustainability [48, 49]. Incorporating features from both the SFW and FCFW, MCFWs provide a unique set of advantages. They combine the rapid deposition rates of an FCFW with the streamlined operation of an SFW. When comparing deposition rates, a 1.2 mm MCFW and a 1.6 mm MCFW are superior to both an SFW and an FCFW [48]. MCFW has quicker travel speeds, greater duty factor, decreased mill scale difficulties, slag-free and spatter-free weld formation, lessened weld flaws like porosity, lack of fusion, and undercut, and eliminates cleaning and post-weld activities like grinding [50, 51]. Due to these features, a 1.2 mm thick metal-cored ‘MEGAFIL 237 M’ wire was used as the wire electrode. The elements of the ASME SA387—Gr. 11—Cl. 2 steel as well as the wire electrode are presented in Table 2. As a shielding gas, 90% argon and 10% carbon dioxide have been combined. The specs of the welding machine are presented in Table 3, and Fig. 3 illustrates how the machine should be configured for the study.

Table 2 Chemical composition of ASME SA387–Gr.11–Cl.2 steel and MEGAFIL 237 M
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Table 3 Continuum 500 welding machine’s specifications
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Fig. 3
figure 3

Miller’s Continuum 500 welding machine

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Adjustments made to the welding variables have a substantial impact on the dynamic properties of GMAW. In terms of voltage, current, shielding gas, the diameter of filler metal, feeder speed, and gas flow rate, these kinds of adjustments can take place. Current (A), voltage (V), and gas flow rate (L/min) were taken into account as the governing variables for the study based on the accessibility and configuration of the welding equipment. Table 4 displays the variations that were made to these variables at three distinct levels.

Table 4 Parameters and their levels
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When preparing and analyzing experimental studies, the design of experiments (DOE) is an essential tool. Since the experimental studies are so time- and resource-intensive, establishments are unable to conduct the trials at all available variable settings and evaluate the optimal potential findings [52,53,54,55,56,57]. Because of this, the importance of DOE cannot be overstated. Some of the DOE methods with their benefits and drawbacks are shown in Fig. 4 [58,59,60,61,62].

Fig. 4
figure 4

General DOE techniques used in engineering applications [58,59,60,61,62]

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Taguchi’s orthogonal array (OA) idea is used here because of its many practical advantages. It’s a simple concept that performs well in a wide range of industrial contexts, thereby making it an adaptable yet uncomplicated method. It improves process or product quality by concentrating on the mean value of an output attribute that is close to the goal value rather than on the value within defined limitations. And despite the fractional nature of the approach, it guarantees parity across all levels of all variables [57, 63,64,65,66]. In light of this, the experimental sets (Table 5) have been arranged according to Taguchi’s L9 OA.

Table 5 Experimental sets based on Taguchi’s L9 OA
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Nine bead-on-plate (BOP) experiments were carried out as per the aforementioned experimental sets utilizing a Continuum 500 welding machine at a steady speed of 8.85 inches per minute (ipm). Figure 5 contains a presentation of the BOP experiments that were conducted.

Fig. 5
figure 5

BOP trials on ASME SA387 Gr.11 Cl.2 steel plates

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Once the plates had cooled, they were sliced to 30 mm x 10 mm (as shown in Fig. 6) using a MAXMEN band saw machine. The output characteristics, including DOP, HAZ, and BW, were measured by inspecting the cut specimens underneath a microscope after they had been polished, etched, and hydrated with water. Figure 7 depicts the measurement terminology for all nine specimens, and Table 6 lists the measured responses.

Fig. 6
figure 6

Sample preparation for Macroscopy

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Fig. 7
figure 7

Measurement terminology of output responses

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Table 6 Measured output responses
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3 Result and discussion

This section discusses the applied approaches and their outcomes for obtaining the best welding input variables for WBG during RMD welding of ASME SA387 Gr.11 Cl.2 steel. In this context, two statistical optimization techniques namely Utility and TOPSIS have been explored with Taguchi Method.

3.1 Utility function approach

Utility functions are a commonly accepted concept in multi-criteria decision-making (MCDM) problems due to their simplicity and ease of understanding for decision-makers. They do not require any additional constraints beyond the aggregation formula. In the utility-based Taguchi process, an MCDM problem can be transformed into a single response optimization problem using a response function, also known as an arbitrary function, which acts as an overall utility index. The goal is to optimize this function to obtain the solution [67,68,69]. According to the utility function approach [70], if \({A}_{x}\) is the performance indicator of an output response \(x\) and there are \(k\) output characteristics evaluating the data set, the joint utility function can be expressed as follows:

$$U\left({A}_{1}, {A}_{2},\dots \dots \dots {A}_{k}\right)=f\left\{{U}_{1}{(A}_{1}\right), {U}_{2}{(A}_{2}),\dots \dots \dots {U}_{k}{(A}_{k})\}$$
(1)

In Eq. (1), the utility of the \({x}_{th}\) output response is represented by (\({U}_{1}{(A}_{1}\left)\right)\). Equation (2) shows the overall utility function, which is equal to the sum of the utilities of individual output characteristics.

$$U\left({A}_{1}, {A}_{2},\dots \dots \dots {A}_{k}\right)={\sum }_{x=1}^{k}{U}_{x}({A}_{x})$$
(2)

The weightage given to the output responses is based on their relative importance and impact on the process. In this case, the overall utility function can be understood as follows:

$$U\left({A}_{1}, {A}_{2},\dots \dots \dots {A}_{k}\right)={\sum }_{x=1}^{k}{W}_{x}{U}_{x}({A}_{x})$$
(3)

In Eq. (3), \({W}_{x}\) represents the importance or influence assigned to the output response \(x\). The total of all the weights assigned to all the output responses should be 1. The output values are evaluated based on lower and higher values using two random arithmetic values 0 and 9 (preference numbers) as benchmarks. Equation (4) can be used to evaluate the preference number \({N}_{p}\) on a logarithmic scale.

$${N}_{p}=O*\text{log}\frac{{A}_{x}}{{A}_{x}^{{\prime }}}$$
(4)

In Eq. (4), \({A}_{x}\) represents the value of output characteristic \(x\). \({A}_{x}^{{\prime }}\) is the lower value of output characteristic \(x\). \(O\) is a constant and can be calculated using Eq. (5), only if \({A}_{x}= {A}^{*}\)(where \({A}^{*}\) is the optimal value), then \({N}_{p}=9\). Hence

The value of output response \(x\) is represented by \({A}_{x}\) in Eq. (4). The lower value of output response \(x\) is represented by \({A}_{x}^{{\prime }}\). \(O\) is a constant that can be found using Eq. (5) if \({A}_{x}\) is equal to the optimal value, denoted as \({A}^{*}\). If this is the case, then \({N}_{p}\) is equal to 9. Therefore,

$$O= \frac{9}{\text{log}\frac{{A}_{x}}{{A}_{x}^{{\prime }}}}$$
(5)

The utility in its whole is expressed as:

$$U={\sum }_{x=1}^{k}{W}_{x}( {N}_{p})$$
(6)

Under the condition:

$${\sum }_{x=1}^{k}{W}_{x}=1$$
(7)

The S/N ratio concept developed by Taguchi involves three different output characteristics: nominal-is-best (NB), lower-is-better (LB), and higher-is-better (HB). Among these, HB is relevant for evaluating utility functions. Therefore, when maximizing the utility function, the output attributes considered in the assessment process will be automatically optimized, either by being minimized or maximized, depending on the specific situation. The optimization method used is illustrated in Fig. 8.

Fig. 8
figure 8

The flow path of the Utility Taguchi approach

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A series of experiments were conducted using the L9 orthogonal array and the resulting responses, including HAZ, DOP, and BW, were recorded and presented in Table 6. Since these responses conflicted with each other, it was necessary to convert them to a common scale. In this context, the utility function approach was used to combine all the conflicting criteria into a single index called the overall utility. First, the individual utility for each of the responses was determined using Eqs. 4 and 5. For HAZ and BW, lower values were preferable, while a higher value was desired for DOP. As shown in Table 7, all of these responses were converted to a scale ranging from 0 to 9, with 0 representing the lowest utility value and 9 representing the highest. By using Eq. 6, it was then possible to combine all of these responses into a single overall utility index, which is also presented in Table 7. The Taguchi S/N ratio was then applied to the overall utility to find the optimal welding condition. From Fig. 9, it was determined that the optimal welding condition is a current of 135 A, a voltage of 14 V, and a gas flow rate of 13 L/min. Additionally, Table 8 shows that voltage is the variable that has the greatest impact on the results.

Table 7 S/N ratio and predicted S/N ratio for overall utility
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Table 8 S/N ratios mean response table
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Fig. 9
figure 9

Main effect plot for Uoverall

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3.2 TOPSIS method

The TOPSIS method, short for Technique for Order Preference by Similarity to Ideal Solution, is a multi-attribute decision-making technique used to identify the best options for solving a problem within a solution space. It was introduced in 1981 by Ching-Lai Hwang and Kwangsun Yoon and is known for its simplicity and ease of understanding and implementation [71,72,73]. The method involves evaluating the degree of proximity to the ideal solution, which should be as close as possible to the positive ideal solution (made up of the best performance values among all options) and as far as possible from the negative ideal solution (made up of the worst performance values) [73,74,75]. TOPSIS has a wide range of applications, including engineering and design, logistics, marketing, manufacturing, and supply chain management, and it is straightforward to program and use, with a consistent number of steps regardless of the problem size [76, 77]. The method involves converting multiple attributes into a single response through a series of following steps [74]:

Step 1

Creating a decision matrix:

$$D=\begin{array}{c}{A}_{1}\\ {A}_{2}\\ .\\ {A}_{i}\\ .\\ {A}_{m}\end{array}\left[\begin{array}{ccccc}{x}_{11}& {x}_{12}& .& {x}_{1j}& {x}_{1n}\\ {x}_{21}& {x}_{22}& .& {x}_{2j}& {x}_{2n}\\ .& .& .& .& .\\ {x}_{i1}& {x}_{i2}& .& {x}_{ij}& .\\ .& .& .& .& .\\ {x}_{m1}& {x}_{m2}& .& {x}_{mj}& {x}_{mn}\end{array}\right]$$
(8)

\({A}_{i}\) (where \(i\) ranges from \(1\) to \(m\)) represents the potential replacements, and \({x}_{j}\) (where \(j\) ranges from \(1\) to \(n\)) represents the characteristics that relate to the substitute’s performance. The performance of \({A}_{i}\) for attribute \({X}_{j.}\)is represented by \({x}_{ij}\).

Step 2

Decision matrix normalization;

$${r}_{ij}=\frac{{x}_{ij}}{\sqrt{{\sum }_{i=1}^{m}{x}_{ij}^{2}}}$$
(9)

\({r}_{ij}\)represents the performance of \({A}_{i}\) normalized for attribute \({X}_{j.}\)

Step 3

Assigning weightage to the normalized decision matrix:

$$V=\left[{v}_{ij}\right]V={w}_{j}{r}_{\begin{array}{c}ij\\ \end{array}}$$
$$D=\left[\begin{array}{ccccc}{y}_{11}& {y}_{12}& .& {y}_{1j}& {y}_{1n}\\ {y}_{21}& {y}_{22}& .& {y}_{2j}& {y}_{2n}\\ .& .& .& .& .\\ {y}_{i1}& {y}_{i2}& .& {y}_{ij}& .\\ .& .& .& .& .\\ {y}_{m1}& {y}_{m2}& .& {y}_{mj}& {y}_{mn}\end{array}\right]$$
(10)

where, \({\sum }_{j=1}^{n}{w}_{j}=1\)

Step 4

Identifying the most favorable (positive best) and least favorable (negative worst) solutions.

  1. a)

    Most favorable solution:

$${A}^{+}=\left\{\left(\underset{i}{max}{y}_{ij}\left|j\in J\right.\right),\left(\underset{i}{min}{y}_{ij}\left|j\in {J}^{{\prime }}\right|i=\text{1,2},\dots \dots \dots,m\right)\right\}$$
(11)
$$=\left\{{y}_{1}^{+},{y}_{2}^{+},\dots \dots \dots,{y}_{j}^{+},\dots \dots \dots{y}_{n}^{+}\right\}$$
  1. b)

    Least favorable solution:

$${A}^{-}=\left\{\left(\underset{i}{min}{y}_{ij}\left|j\in J\right.\right),\left(\underset{i}{max}{y}_{ij}\left|j\in {J}^{{\prime }}\right|i=\text{1,2},\dots \dots \dots,m\right)\right\}$$
(12)
$$=\left\{{y}_{1}^{-},{y}_{2}^{-},\dots \dots \dots,{y}_{j}^{-},\dots \dots {y}_{n}^{-}\right\}$$

where,

\(J=\left\{j=\text{1,2},3,\dots \dots \dots,n\left|j\right.\right\}:\) beneficial features

\({J}^{{\prime }}=\left\{j=\text{1,2},3,\dots \dots \dots,n\left|j\right.\right\}:\) nonbeneficial features

Step 5

Measuring the distance between substitutes and the ideal solution. The distance between each substitute and the ideal solution is determined using n-dimensional Euclidean distance calculations using these equations.

$${S}_{i}^{+}=\sqrt{{\sum }_{j=1}^{n}{\left({y}_{ij}-{y}_{j}^{+}\right)}^{2}}i=\text{1,2},\hspace{0.33em}\dots \dots \dots,m$$
(13)
$${S}_{i}^{-}=\sqrt{{\sum }_{j=1}^{n}{\left({y}_{ij}-{y}_{j}^{-}\right)}^{2}}i=\text{1,2},\hspace{0.33em}\dots \dots \dots,m$$
(14)

Step 6

Evaluation of the overall performance coefficient nearest to the ideal solution.

$${C}_{i}^{+}=\frac{{S}_{i}^{-}}{{S}_{i}^{+}+{S}_{i}^{-}},i=\text{1,2},\dots \dots \dots,m;0\le {C}_{i}^{+}\le 1$$
(15)

A flow diagram of the optimization process used in this study is shown in Fig. 10.

Fig. 10
figure 10

TOPSIS method’s flow path

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The experiments were conducted using the L9 orthogonal array, and the results (HAZ, DOP, and BW) were recorded and presented in Table 9. The results were then normalized using Eq. 9 and the normalized values are shown in Table 9. In this study, all of the responses were given equal importance, so equal weightage was assigned to each response using Eq. 10 (shown in Table 9). Since the responses are conflicting, it is necessary to determine the most favorable and least favorable solutions (shown in Table 10) using Eqs. 11 and 12, respectively. In this context, lower values for HAZ and BW were preferred, so the lowest values for these responses were considered the most favorable solutions and vice versa. Similarly, higher values for DOP were preferred, so the highest value for DOP was considered the most favorable solution and vice versa. The separation distance from the positive and negative ideal solutions was then calculated using Eqs. 13 and 14, respectively, and listed in Table 11. The closeness coefficient was then determined using Eq. 15, with the highest value being the preferred result. Finally, the Taguchi method of S/N ratio was applied to the closeness coefficient to determine the optimal welding combination, which was found to be a current of 135 A, a voltage of 14 V, and a gas flow rate of 13 L/min (shown in Fig. 11). The predicted S/N ratio was also calculated to validate the optimal combination, and it was observed from Table 11 that the predicted S/N ratio was higher than the other computed S/N ratios, supporting the chosen optimal combination. The mean response table in Table 12 shows that voltage is the most significant governing variable.

Table 9 Experimental data for normalization and assigned weightage
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Table 10 Most favorable (positive best) and least favorable (negative worst) solutions
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Table 11 The separation distance from the most favorable (positive best) and least favorable (negative worst) solutions together with closeness coefficient and S/N ratios
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Table 12 S/N ratios mean response table
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Fig. 11
figure 11

Main effects plot for parametric settings

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4 Conclusions

This study evaluates and optimizes current, voltage, and gas flow rate for regulated metal deposition (RMD) welding on ASME SA387 Gr. 11 Cl. 2 steel in terms of the heat-affected zone (HAZ), depth of penetration (DOP), and bead width (BW). The following conclusions are derived:

  1. i.

    Using a dual-pronged optimization approach (Utility-Taguchi and TOPSIS with Taguchi S/N ratio), this study identified the optimal welding parameters as 135 A current, 14 V voltage, and 13 L/min gas flow rate.

  2. ii.

    Analysis of the S/N ratio revealed voltage as the most influential factor, highlighting its critical role in controlling HAZ, DOP, and bead width.

  3. iii.

    The established methods offer a reliable framework for determining optimal RMD welding conditions in various applications.

  4. iv.

    Implementing these optimized parameters can enhance welding integrity, and worker safety, and pave the way for sustainable manufacturing and continuous quality improvement in pipeline welding across various industries.

The work may further be extended by investigating the applicability of these optimization methods to other steel grades and material types beyond ASME SA387 Gr.11 Cl.2. Development and validation of predictive models and simulations can further optimize RMD welding settings and exploring the relationship between process parameters and microstructure/mechanical properties.