Plane Thermoelastic Waves in Infinite Half-Space Caused Decision Making: Applications in Management and Engineering Vol. 5, Issue 2, 2022, pp. 316-328. ISSN: 2560-6018 eISSN: 2620-0104 DOI: https://doi.org/10.31181/dmame0318062022c * Corresponding author. E-mail address: sudiptohaki@hotmail.com (S. Chaki), dbose@nitttrkol.ac.in (D. Bose) OPTIMISATION OF SPOT-WELDING PROCESS USING TAGUCHI BASED CUCKOO SEARCH ALGORITHM Sudipto Chaki1* and Dipankar Bose2 1Automobile Engineering Department, MCKV Institute of Engineering, India, 2 Mechanical Engineering Department, National Institute of Technical Teachers Training and Research, India Received: 2 February 2022; Accepted: 8 June 2022; Available online: 18 June 2022. Original scientific paper Abstract: The present work evaluated the efficiency of a Taguchi-based Cuckoo Search (CS) algorithm for optimizing the spot-welding process. The L9 orthogonal array of the Taguchi method is used for the conduction of required experiments. During the study input parameters are welding current (kA), hold time (cycles), welding time (cycles), and electrode pressure (kPa) while Peak Load, kN has been considered as an output parameter. The required objective function is developed through regression model formulation. Initially, CS operating parameters such as maximum number of iterations, number of nests, and probability to discover a cuckoo egg by host bird is optimized through the Taguchi method and are found as 40, 20, 0.5 respectively. That optimized CS further optimizes the spot-welding process. The maximum peak load of 34.5 kN is obtained if the welding current is 30.7 kA, welding time is 32 cycles, hold time is 20 cycles, and electrode pressure is 480 kPa respectively. Experimental validation yields a very low % error of 1.93% during optimization with an optimized CS method and while the error is substantially high if optimization is conducted using a non-optimized CS method Key words: Spot welding, Cuckoo Search method, Taguchi method, optimization, Peak load. 1. Introduction Spot welding is a popular electric resistance welding process in which workpieces are held together under pressure exerted by electrodes and metal surface points in contact are get joined by the heat obtained from resistance to electric current. It is a mailto:sudiptohaki@hotmail.com mailto:dbose@nitttrkol.ac.in Optimization of Spot-Welding Process Using Taguchi Based Cuckoo Search Algorithm 317 quick process and enables the easier joining of even dissimilar metals. The process is widely applied in the automotive sector. The controllable parameters of spot welding such as electrode tip diameter, weld nugget, weld current, holding time, cycle time, etc, bear a very complex relationship between them. In the recent past, researchers employed the conventional statistical design of experiment (DOE) based techniques like the Taguchi method, Response Surface Methods (RSM), Grey Relational Analysis (GRA), etc to optimize spot-welding process parameters. Attempts to optimize tensile strength for spot-welded joints of Titanium alloy [Bozkurt and Çakır (2021), Fatmahardi et al (2021)], aluminum alloys [Raheem, (2021)], dissimilar materials combining steels and composites [Neystani et al. (2019)], steels [Tyagi et al.(2022), Kumar et al. (2021), Ebrahimpour et al (2021)], have been computed through the Taguchi method [Bozkurt and Çakır (2021), Fatmahardi et al (2021), Neystani et al. (2019), Tyagi et al.(2022), Kumar et al. (2021)] and RSM [Raheem, (2021), Ebrahimpour et al. (2021)]. But such processes generally involve high mathematical complexity among operating parameters and possible experimental noise. Therefore, the application of those traditional statistical optimization methods is often found inadequate for their inability to reach global minima for the multimodal problem. Soft computing techniques involving genetic algorithm (GA), simulated annealing (SA), particle swarm optimization (PSO), etc can be efficiently employed for optimizing such highly non-linear problems with improved accuracy. The same has been employed already for Electric Discharge Machining (EDM) [Chinmaya et al. (2017)], Laser material processing [Chaki et al. (2012)], submerged arc welding, etc [Choudhary et. Al. (2020)]. However, limited applications of such algorithms are found in the spot-welding domain. Recently, the tensile strength of spot-welded joints for mild steel was optimized by Pattanaik et al. (2018) using L25 Taguchi-based GRA and GA. Cao et al. (2021) optimized spot-welded joint strength of aluminum to steel using a GA and RSM. Dhawale et al. (2019) optimized the strength of spot-welded joints using PSO and experimental validation incurred negligible error with 0.57% error. Zhao et al. (2014) optimized failure energy of spot-welded titanium alloy joints using Box–Behnken L17 experimental design of RSM and artificial fish swarm algorithm. The literature survey indicates applications of several conventional statistical methods including Taguchi, RSM, etc to optimize the resistance spot welding processes [Bozkurt and Çakır (2021), Fatmahardi et al (2021), Neystani et al. (2019), Tyagi et al. (2021), Kumar et al. (2021)] Raheem, (2021), Ebrahimpour et al. (2021)]. However, those optimization processes have inherent limitations to stuck into local minima often resulting in faulty optimized output for multimodal problems. However, further nature-inspired algorithms like GA, PSO, SA etc. are used for solving spot welding [Pattanaik et al. (2018), Cao et al. (2021), Dhawale et al. (2019), Zhao et al. (2014)] and similar problems [Chinmaya et al. (2017), Chaki et al. (2012), Choudhury et al. (2020)] with greater accuracy where process parameters bear complex mathematical relationships among them. But, the optimization performance of those algorithms is governed by several operating parameters, whose selection is generally user-dependent. Its wrong selection often leads to inadequate optimization output. Therefore, prior optimization of those controlling parameters is necessary and if operated through an optimized parameter setting then only the best-optimized output from the algorithm may be obtained. However, such optimized nature-inspired algorithms are not employed so far for the spot-welding process. Cuckoo Search (CS) [Yang & Deb (2010)], a biologically inspired method for optimization is controlled by certain parameters like the number of nests, iterations, the probability with which the host bird discovers the cuckoo egg in nests, etc. CS is employed in the field of Time Chaki and Bose /Decis. Mak. Appl. Manag. Eng. 5 (2) (2022) 316-328 318 series and forecasting [Jiang et al. (2016), Xiao et al. (2017)], Data mining [Swathypriyadharsini & Premalatha (2021)], non-traditional machining [Saravanan et al. (2020), Shastri & Mohanty (2021)], Scheduling [Gu et al. (2021)] etc. Present work employed an optimized CS algorithm to optimize the spot-welding process. The Taguchi method optimized the CS algorithm during the study. Such Taguchi optimized CS is not employed earlier for optimizing the spot-welding process. Further, the performance of that optimized CS is compared with a non-optimized CS to understand the usefulness of the proposed method. 2. Methodology A Taguchi integrated cuckoo search (CS) optimization method is employed for optimizing the RSW process using an optimized CS. The controllable input parameters in the RSW process are welding current, kA (I) 2) welding time, cycles (WT), 3) hold time, cycles (HT), and 4) electrode pressure, kPa (EP) while tensile strength is the output parameter. Further optimization of spot welding is computed through the following steps: i) Conduction RSW experiments using Taguchi L9 experimental design matrix to generate an input-output dataset. ii) Objective function formulation through developing suitable regression equation iii) Optimization of CS parameters through Taguchi method for determining an optimized CS algorithm iv) Optimizing the spot-welding process using that optimized CS algorithm and determining the model efficiency through experimental validation. The outline of the process has been given in Fig.1. Detailed steps for Taguchi integrated cuckoo search (CS) optimization method are given as follows: Step A: Development of the experimental dataset I. Generate Taguchi L9 design matrix II. Conduct experiments following experimental design III. Measure output characteristics IV. Generate the input-output dataset Step B: Formulation of the objective function I. Normalize input-output dataset between 0 and 1. II. Develop Regression model using the normalized dataset 𝑌 = 𝑓(𝑥1, 𝑥2, . . , 𝑥𝑛 ) + 𝜀, where, (x1,x2,…,xn) are n number of independent input variables, Y produces a certain response, 𝜀 represents noise or error in the response y. III. Consider it as the objective function for the Cuckoo search (CS) algorithm. Step C: Optimization of Cuckoo search (CS) parameters I. Generate Taguchi L9 design matrix for a) Maximum iteration numbers (Imax) , b) Number of nests (N), c) probability to discover a cuckoo egg by host bird (pa) II. For (i=1 to 9) { Select Imax, N, and pa as CS input parameters Call CS subroutine Store optimum fitness function value as output for ith set of input parameters } Optimization of Spot-Welding Process Using Taguchi Based Cuckoo Search Algorithm 319 III. Dataset is generated with Imax, N and pa as inputs (xi’s)and Fitness function as output parameter (Yi) IV. Compute Taguchi quality loss function and normalise for all Yi’s V. Compute signal to noise ratio (S/N ratio) VI. Compute level wise mean of S/N ratio for each factor VII. Determine optimized Imax, N and pa Step D: Process optimization with optimized CS algorithm I. Set, Imax, N and pa, at optimized value as determined in Step C II. Call CS subroutine III. Determine optimized fitness function value (# such as maximum tensile strength or Peak Load of RSW joint in present work) Cuckoo Search (CS) subroutine Begin Set, the objective function using the regression equation developed in step B Maximum iteration numbers (Imax) Number of nests (N) Probability to discover a cuckoo egg by host bird (pa) Iterate: generate randomly a cuckoo (i) from lev՜y flight Evaluate fitness function value (Fi) randomly select nest j and determine fitness function value (Fj) if (Fi < Fj) replace j using the new solution end Abandon worst nests by a fraction pa Randomly generate new solution from all cuckoos Fitness evaluated Keep the Better solutions Current best is found through ranking Continue (until Iteration > Imax) Figure 1. Outline of the Taguchi based cuckoo search algorithm Cuckoo Search (CS) Algorithm Objective function formulation Regression model development Taguchi method for CS parameter setting Quality loss function computation Experimental dataset generation Optimized parameter setting for CS Spot welding process optimisation with optimised CS Chaki and Bose /Decis. Mak. Appl. Manag. Eng. 5 (2) (2022) 316-328 320 2.1. Experiment A resistance spot welding setup (manufactured by Electro Weld Industries) operated by AC (50 Hz) 200 KVA rating (@ 50% duty cycle) is used for conducting experiments using 3 levels, 4-factor experimental design on mild steel (IS 2062, Gr. B) having block dimensions 100mm x 25mm x3mm. The experimental setup used is given in Fig.2. Figure 2. Experimental setup Table 1 specifics the values of control factors at different levels. The possible variations of control factors for Table1 have been determined through pilot experiments. Altogether nine experiments are conducted using Taguchi L9 experimental design. The input parameters considered during experimentation are, 1) welding current, kA (I) 2) welding time, cycles (WT), 3) hold time, cycles (HT), and 4) electrode pressure, kPa (EF). For welded joints, the output parameter is the ultimate tensile strength which is the maximum force required to tear the spot joints from each other. A Universal Testing machine measured it through peak load, kN (L). Table 2 furnishes the experimental dataset. Input and output parameters are as follows: X = [I WT HT EP], 𝑌 = [𝑃𝐿] Optimization of Spot-Welding Process Using Taguchi Based Cuckoo Search Algorithm 321 (a) Before (a) After Figure.3. Job specimen before and after resistance spot welding Table 1. Control factors with their levels Control Factors Symbol Level of Control Factors Level 1 Level 2 Level 3 Welding Current, kA I 29.5 30 30.7 Welding Time, cycles WT 25 28 32 Welding Hold time, cycles HT 20 25 30 Electrode pressure, kPa EP 480 550 620 2.2. Development of regression model A first-order regression model with interaction effects is developed to determine the approximate relationship between four input variables and the output variable. The experimental dataset is normalized prior development of the model to ensure better optimization performance. The input and output variables are normalized as follows before modeling: Xnor = X − Xmin Xmax − Xmin Ynor = Y Ymax ⁄ (2) Where Xmax and Xmin represent the maximum and minimum values of the input parameters and Ymax represents the maximum value of the output parameter. The model is developed using Minitab16 software has been given below: 𝑃𝐿 = 0.592122 + 0.387324 × I + 0.307468 × WT + 0.521117 × HT − 0.117952 × EP − 0.0806291 × I × WT − 0.430832 × I × HT − 0.556653 × WT × HT (3) The model is evaluated by the regression coefficient (R-square) value. R2 and R2 (adjusted) values obtained are 0.9715 and 0.7731 respectively. Near unity R2 and R2 (adjusted) value indicates the developed model is adequate. Chaki and Bose /Decis. Mak. Appl. Manag. Eng. 5 (2) (2022) 316-328 322 Table 2. Input design matrix and experimental details Trial No. Input parameters Output parameter Welding current, kA Welding Time, cycles Welding Hold time, cycles Electrode Pressure, kPa Peak Load KN I WT HT EP PL 1 29.5 25 20 480 17.15 2 29.5 28 25 550 21.55 3 29.5 32 30 620 21.5 4 30 25 25 620 23.8 5 30 28 30 480 28.5 6 30 32 20 550 28.25 7 30.7 25 30 550 28.6 8 30.7 28 20 620 27.15 9 30.7 32 25 480 27.6 Maximum value 30.7 32 20 480 28.6 Minimum value 29.5 25 30 620 - 2.3. Formulation of objective function It is intended to maximize the tensile strength of the joint in terms of peak load. The objective functions along with constraints are given below: The objective functions: Maximize PL (I, WL, HT, EP) Subject to constraints: 29.5 ≤ I ≤ 30.7 25 ≤ WT ≤ 32 20 ≤ HT ≤ 30 480 ≤ EP ≤ 620 (4) However, as the CS algorithm is inherently developed for minimization problems, the –ve sign is incorporated before the output variable to convert it into a maximization problem. Along with, as regression model is formed with normalized dataset the objective function and constraints have been reduced into the following form: Minimize: 𝑃𝐿 = −(0.592122 + 0.387324 × I + 0.307468 × WT + 0.521117 × HT − 0.117952 × EP − 0.0806291 × I × WT − 0.430832 × I × HT − 0.556653 × WT × HT) Subject to constraints: 0 ≤ I, WT, HT, EP ≤ 1 (5) Optimization of Spot-Welding Process Using Taguchi Based Cuckoo Search Algorithm 323 2.4. Cuckoo Search Algorithm Cuckoo search (CS) [Yang & Deb (2010)] is a nature-inspired metaheuristic algorithm based on the brood parasitism characteristics observed in cuckoo species by which it can lay its eggs in the nests of other host birds (often other species). Upon discovering the eggs do not belong to them, the host bird will remove those eggs from nests, or move to another nest leaving that nest. The probability of discovering the egg laid by a cuckoo by the host bird is pa ∈ [0, 1]. Here, each nest refers to one egg that also refers to one cuckoo. During optimization, n numbers of host nests (xi, i=1,….,n) are randomly selected as the initial population and fitness value (Fi) of eggs of host nests are computed. Further, the new nest is randomly generated by a cuckoo(i) through levy flight using the equation, 𝑥𝑖 𝑡+1 = 𝑥𝑖 𝑡 + 𝛼 ⊕ 𝐿�́�𝑣𝑦(𝜆) where, where α > 0 indicates the step size of steps, t represents iteration number, and random walk-through Lévy flight (λ) is accomplished by a Lévy distribution of 𝐿�́�𝑣𝑦~𝑢 = 𝑡−𝜆, (1 < λ ≤ 3). Further, corresponding to updated solution points (nests) fitness value (Fj) of eggs is computed. Upon comparing with the initial fitness value (Fi), if improvement in fitness value is observed, the updated solution is accepted. During computation, the pa fraction of the worst nests is abandoned. Repetition of the above process is continued till stopping criteria are achieved. Here, controllable parameters are the maximum number of iterations, number of nests, and probability to discover a cuckoo egg by host bird (pa). 2.5. Taguchi Method for optimization of CS parameters Taguchi’s method studies the entire factor space through a limited set of experiments based on an orthogonal array. The method designates the desirable value of output as ‘signal’ and the undesirable value as ‘noise’. The term ‘signal-to-noise ratio’ or S/N ratio is an indicator of the deviation of output from the desired value. L 9 orthogonal array, based on three levels three factors experimental design is used. Factors are the maximum iteration numbers (I), the number of nests (N), and the value of pa respectively. The numeric value of variables at different levels is furnished in Table 3. For a specific set of factor values, CS computes optimized objective function value PL and employs it for computing loss function. For maximization of PL higher- the-better quality characteristic is required and the loss function (f i) can be given as: 𝑓𝑖 = 1 𝑛 ∑ 1 𝑦𝑖 2 𝑛 𝑖=1 (6) Where, yi is the observed output at the ith trial, and n is the number of trials. Quality loss functions obtained are normalized and signal to noise ratio or S/N ratio (SNR) is calculated corresponding to ith trial condition as: SNR𝑖 = −10 log10(𝑓i) (7) 3. Results and Discussion 3.1. Optimization of CS parameters using Taguchi method The Taguchi design matrix with control parameter settings of CS has been shown in Table 3. A program code for CS is developed in MATLAB2010 using the objective Chaki and Bose /Decis. Mak. Appl. Manag. Eng. 5 (2) (2022) 316-328 324 function developed (Eq.5). Further, the program is run for each parameter setting of CS given in Table 4 to find the corresponding objective function value (PL). It is further evaluated for determining the quality loss function, its normalization, and signal-to- noise ratio using Eq. (6) - Eq. (7) and shown in Table 4. Table 3. CS parameters with different levels Symbol CS parameters Level 1 Level 2 Level 3 Imax Maximum iteration numbers 20 30 40 N Number of nests 10 20 30 pa Probability to discover a cuckoo egg by host bird 0.1 0.3 0.5 Table 4. Quality loss values with S/N ratio using L9 orthogonal array Exp no. Coded Input Parameters Output Parameter Quality Loss Normalized Quality Loss SNR (dB) Imax N Pa Objective Fn (PL) 1 1 1 1 -1.1848 0.7124 1.0000 0.0000 2 1 2 2 -1.1892 0.7071 0.9926 0.0322 3 1 3 3 -1.2042 0.6896 0.9680 0.1411 4 2 1 2 -1.1922 0.7036 0.9876 0.0541 5 2 2 3 -1.2053 0.6884 0.9663 0.1490 6 2 3 1 -1.1951 0.7002 0.9828 0.0752 7 3 1 3 -1.2029 0.6911 0.9701 0.1317 8 3 2 1 -1.2021 0.6920 0.9714 0.1259 9 3 3 2 -1.1885 0.7079 0.9938 0.0271 Further, from the influence of controlling parameters of CS on the S/N ratio (Table 5) the optimized level of CS parameters is determined as follows: Maximum number of iterations (level 3): 40 Number of nests (level 2): 20 Probability to discover a cuckoo egg by host bird, pa (level 3): 0.5 Comparison between optimized CS parameter setting with initial parameter setting indicates reasonable improvement in SNR (i.e. 0.1562) and provided in Table 6. 3.2. Optimization of spot-welding process parameters Finally, the spot-welding process is optimized through an optimized CS with the above-mentioned controlling parameter setting. Fig.2 shows the nature of variation of the best function value with iterations leading to convergence. Optimization of Spot-Welding Process Using Taguchi Based Cuckoo Search Algorithm 325 Table 5. Effect of factors on S/N ratio Factor Mean of S/N ratio (dB) Maximum - Minimum Rank Level 1 Level 2 Level 3 Maximum iteration numbers (Imax) 0.1733 0.2783 0.2847a 0.1114 2 Number of nests (N) 0.1858 0.3071a 0.2433 0.1213 3 probability to discover a cuckoo egg by host bird (pa) 0.2011 0.1134 0.4218a 0.3084 1 a Optimum level Table 6. Improvement in performance at the optimum parameter level Figure 4. Performance of optimized CS during optimisation The optimized (maximum) value of PL is found as 1.2063. The optimized value peak load (PL) after denormalization is 34.5 kN with corresponding operational input parameter welding current (I), welding time (WT), hold time (HT), and electrode pressure (EP) values as, 30.7 kA, 32 cycles, 20 cycles, and 480 kPa respectively. Upon comparing the operational input parameter setting with corresponding level values provided in Table 1 it has been found that the maximum peak load indicator of ultimate tensile strength of the joint will be obtained at high welding current, high welding time, Low hold time, and low electrode pressure. A validation experiment is conducted with optimized parameter setting and compared with optimized output for evaluating the accuracy of the optimized CS algorithm and furnished in Table 7. The 0 10 20 30 40 -1.25 -1.2 -1.15 -1.1 -1.05 -1 Number of Iterations O b je c ti v e F u n c ti o n V a lu e Best Function Value : -1.2063 Initial Parameter Setting Optimal CS parameters Level I1N1pa1 I3N2pa3 PL -1.1848 -1.2063 MSNR (dB) 0 0.1562 Improvement of SNR (dB) 0.1562 Chaki and Bose /Decis. Mak. Appl. Manag. Eng. 5 (2) (2022) 316-328 326 optimized CS method can predict optimized output with an absolute % error of 1.93%. Computation has been conducted using a Pentium IV, 3 GHz, and 512 MB PC. Table 7. Results of spot-welding optimization using optimized CS and experimental validation Operational Input Parameters Output Parameter Welding current Welding Time Welding Hold time Electrode Pressure Peak Load kA cycles cycles kPa KN Normalised Value 1 1 0 0 1.2063 Denormalised Value 30.7 32 20 480 34.50 Experimental Value 30.7 32 20 480 35.18 Absolute % Error 1.93 4. Conclusion Present work aimed to develop a Taguchi-based CS algorithm for enhanced optimization performance and employed to optimize spot welding process. The process is intended to maximize the peak load leading to a maximum tensile strength of the welded joint. The conclusions are as follows: (i) Taguchi method determined the optimum value of controllable parameters of CS algorithm such as the number of iterations (Imax), number of nests (N), and probability to discover a cuckoo egg by host bird (pa). An optimum combination of CS parameters with Imax, N, and pa values as 40, 20, and 0.5 respectively will yield the best optimization result for the spot-welding problem under study. (ii) The performance of the CS algorithm is improved considerably with the optimized CS parameter combinations. On comparing that performance with a non- optimized initial parameter setting, an improvement of 0.1562 dB is measured in terms of SNR. (iii) Finally, optimization of spot welding with the optimized CS yields a maximum peak load of 34.5 kN for 30.7 kA welding current, 32 cycles welding time, 20 cycles hold time and 480 kPa electrode pressure. (iv) The maximum peak load for the welded joint is found at high welding current, high welding time, Low hold time, and low electrode pressure. (v) Experimental validation of the optimized result indicates a low error of 1.93% which signifies the accuracy of the model. (vi) The Taguchi-based CS algorithm may be used effectively for any other process. The process may be further extended to optimize operating parameters of other popular algorithms like the water cycle algorithm, krill herd algorithm, mine blast algorithm, interior search algorithm, etc. Author Contributions: Conceptualization, S.C. and D.B.; methodology, S.C..; software, S.C.; validation, S.C. and D.B.; formal analysis, S.C. and D.B.; investigation, D.B.; resources, S.C..; writing—original draft preparation, S.C.; writing—review and editing, S.C. and D.B.; All authors have read and agreed to the published version of the manuscript. Optimization of Spot-Welding Process Using Taguchi Based Cuckoo Search Algorithm 327 Funding: This research received no external funding. Acknowledgments: Authors would like to thank the National Institute of Technical Teachers’ Training and Research, Kolkata for providing necessary technical support. 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