OPTIMIZATION OF RESISTANCE SPOT WELDING PROCESS
USING TAGUCHI METHOD AND A NEURAL NETWORK
T
here has been a significant increase in the use ofhigh-strength steel sheet in the automobile industry to permit reductions in thickness and thus in vehicle weight.1 The substitution of high-strength steel sheet for thicker plain carbon steels helps to lower weight and meet federally-mandated improvements in fuel economy. Resistance welding is widely used in mass production, in which production runs with a consistent condition. The resis-tance spot welding (RSW) process is especially used in the automobile industry.2 However, high-strength steel sheet has narrow welding current ranges in the RSW process. Sometimes, this limited weldability is a consequence of the interfacial failure of the weld nugget, producing an appar-ently smaller fusion zone.3The physical variables of the metal may include not only the composition of the steels but also the surface condition. Surface effects have been studied and found to have noticeable effects on spot weldability.4In summary, it is not easy to obtain optimal parameters of the RSW process on high-strength steel sheet.
Many parameters affect the RSW quality for high-strength steel sheet, such as welding current, electrode force, welding time, and so forth. The desired welding parameters are usually determined based on experience or handbook values. How-ever, it does not ensure that the selected welding parameters result in optimal or near-optimal welding quality character-istics for the particular welding system and environmental conditions. The Taguchi method, a popular experimental de-sign method applied in industry, can alleviate the dis-advantages of full factorial design and approaches the optimization of parameter design, although the number of experiments is reduced.5However, the Taguchi method has certain limitations when used in practice. The optimal solu-tions were only obtained within the specified level of control factors. Once the parameter setting is determined, the range of optimal solutions is constrained concurrently. The Taguchi method is unable to find the real optimal values when the specified parameters are continuous in nature because it only addresses the discrete control factors. Neural network (NN) technique with nonlinear function is capable of accurately representing the complex relationship between inputs and outputs.6–8The trained neural model was also used to accu-rately predict the response at given parameter settings. In addition, Khaw et al.9proved that benefits could be obtained using the Taguchi concept for NN design. First, this method-ology is the only known method for NN design that considers robustness. It enhances the quality of the NN designed. Sec-ond, the Taguchi method uses orthogonal arrays (OAs) to sys-tematically design an NN. Subsequently, the design and development time for NNs can be reduced tremendously. In this study, an application involving combination of the Taguchi method and an NN to determine optimal condition for improv-ing the RSW process quality of high-strength steel sheet was presented. The experimental procedure showed that the
Taguchi method not only provides systematic and efficient methodology for the initial optimization of the RSW process parameters but is also employed to find out the primary influ-encing parameters such as welding current and the size of electrode tip that affects tensile shear strength of specimen. A proposed approach that combined the Taguchi method and an NN then was used to resolve the limitations of applying the said method only. This was done instead of the basic back-propagation (BP) algorithm (gradient descent algorithm). The Levenberg–Marquardt backpropagation (LMBP) algo-rithm with high speed for convergence was adopted. The NN package software MATLAB Neural Network Toolbox (The MathWorks, Inc., Natick, MA) was used to develop the required network. The experimental results were conducted to verify the optimal welding parameter.
INITIAL OPTIMIZATION BY TAGUCHI METHOD
The high-strength steel sheet was used in this study; its chem-ical composition is listed in Table 1. Plates 0.7 mm in thickness were cut into strips of size 30 3100 mm. The resistance spot welder (FANUC a8/4000is type) had been utilized for the experiment. The schematic diagram of high-strength steel sheet specimen for resistant spot welding is shown in Fig. 1.
Quality Characteristic and Parameters
of RSW Process
The study used tensile shear strength of specimens as the quality characteristic in the process. A universal testing machine (MTS 810, MTS Systems Corporation, Eden Prairie, MN) had been used for this study to measure the welding tensile shear strength of the RSW specimens. The speed was set at 0.1 mm/s in the testing. Dr. Taguchi separated all the influencing factors into two main groups, the control factors and noise factors. Control factors are those that allow a man-ufacturer to control during processing and the noise factors are expensive or difficult to control.10As learned from hand-book and the practical experience in the production of auto-body, the major welding parameters for the processing quality of weldment include welding current, welding time, electrode force, the size of electrode tip, and surface condition of speci-mens in the RSW process. By making reference to the existing parameter conditions in the production line, the range of experimental parameter value has been initially framed as below: welding current 6200–11,000 A, welding time 8–26 cycles, electrode force 1.8–3.3 kN, and the size of electrode tip f3–f6 mm. The value of each welding process parameter at the different levels is listed in Table 2. Surface condition of the welding area was selected as the noise factor in this study. The specimens at level 1 (N1), without any cleaning treat-ment, may have been tarnished with dirt and/or grease. The surface impurities were removed and the surface cleaned with acetone at level 2 (N2). The initial conditions of production operation currently were welding current at 7800 A, welding time at eight cycles, electrode force at 1.8 kN, and the size of electrode tip at f4 mm.
H.-L. Lin, T. Chou, and C.-P. Chou are affiliated with the Department of Mechan-ical Engineering, National Chiao Tung University, Hsinchu, Taiwan.
OA Experiment
Taguchi had tabulated 18 basic OAs that are called standard OAs.10Four four-level control factors, in addition to one noise factor, were considered in this investigation. The interaction effect between the welding parameters was not considered. Therefore, there are 12 degrees of freedom owing to the four control factors. The degrees of freedom for the OA should be greater than or at least equal to those for the process param-eters. L16 (45) OA that has 15 degrees of freedom was employed in this study. An experimental layout with an inner array for control factors and an outer array for a two-level noise factor (N1 and N2) is shown in Table 3. Four repetitions (y1, y2, y3, and y4) for each trial are used with this experimen-tal arrangement; y1and y2are N1 specimens (without clean-ing); y3and y4are N2 specimens (cleaned with acetone). The experimental results for the tensile shear strength using L16 OA are shown in Table 4.
Evaluation of Initial Optimal Condition
Taguchi has created a transformation of the repetition data to another value, which is to say a measure of the variation present. The transformation is the signal-to-noise ratio (SNR).11 There are several SNRs available, depending on the type characteristic being present, such as lower is better (LB), nominal is best (NB), or higher is better (HB). The ten-sile shear strength of the specimens as discussed earlier belongs to the higher-is-better quality characteristic. The SNRs, which condense the multiple data points within a trial, depend on the three-characteristic LB, NB, and HB. The equation for calculating the SNR for HB characteristic is:
SNR 5 2 10log 1 n+ n i 5 1 1 y2 i ð1Þ
where n is the number of tests in a trial (number of repetitions regardless of noise levels). The value of n is 4 in this study. The SNRs corresponding to the tensile shear strength value of each trial is shown in Table 4. The effect of each welding pro-cess parameter on the SNR at different levels can be sepa-rated out because the experimental design is orthogonal. The description of the SNR for each level of the welding pro-cess parameters is summarized in Table 5. Figure 2 shows the SNR graph obtained from Table 5. Basically, the larger the SNR, the better the quality characteristic (tensile shear strength) for the specimens. The initial optimal conditions of the RSW process parameter levels, A1B4C1D3, can be deter-mined from Fig. 2.
Analysis of Variance
The purpose of the analysis of variance (ANOVA) is to inves-tigate welding process parameters, which can significantly affect the quality characteristics.12The percent contribution in the total sum of the squared deviations can be used to evaluate the importance of the welding process parameter change on these quality characteristics. When the contribu-tion of a factor is small, as with factor D (welding time) in Table 6, the sum of squares for that factor is combined with the error. This process of disregarding the contribution of a selected factor and subsequently adjusting the contributions of the other factors is known as ‘‘pooling.’’11The welding cur-rent and the size of electrode tip were the significant welding
Table 1—Chemical composition of the material
used (wt%)
MATERIAL C Si Mn P S Fe
MJSC340D 0.062 0.48 0.95 0.013 0.004 Balance
Table 2—Control factors and its levels
FACTOR
PROCESS
PARAMETER LEVEL 1 LEVEL 2 LEVEL 3 LEVEL 4
A The size
of electrode tip
f3 mm f4 mm f5 mm f6 mm
B Welding current 6200 A 7800 A 9400 A 11000 A
C Electrode force 1.8 kN 2.3 kN 2.8 kN 3.3 kN
D Welding time 8 cycles 14 cycles 20 cycles 26 cycles
Fig. 1: Schematic diagram of the specimens
Table 3—Summary of experimental layout
using an L16 OA
TRIAL NO.
NOISE FACTOR
CONTROL FACTOR N1 SPECIMENS N2 SPECIMENS A B C D y1 y2 y3 y4 1 1 1 1 1 Measure data 2 1 2 2 2 3 1 3 3 3 . . . . . 15 4 3 2 4 16 4 4 1 3
parameters in affecting the quality characteristic, with the welding current being the most significant, as indicated by Table 6.
Confirmation Test and Proper Regulation
The final step of the Taguchi method is to compare the esti-mated value with the confirmative experimental value, using the optimal level of the control factors to confirm with the experimental reproducibility. The estimated SNR hoptusing the optimal level of the control factors, can be calculated as:
hopt5 hˆ1 + q
j51
ðhj2 hˆÞ ð2Þ
where hˆ is the total average of SNR of all the experimental values, hjthe mean SNR at the optimal level, and q the
num-ber of the control factors that significantly affect the quality characteristic. Refering to Tables 4 and 5, estimated SNR hopt is computed as:
hopt5 11:213 1ð11:941 2 11:213Þ 1 ð12:252 2 11:213Þ 5 12:98ðdBÞ
The confidence interval (CI) is a maximum and minimum value between which the true average should fall at some stated percentage of confidence.11 The confidence limits of the above estimation can be calculated taking into account the following equation:
CI 5 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Fa;1;veVep 1 neff 11 r s ð3Þ
where Fa;1;veis the F ratio required for a 5 0.05 (with a confi-dence of 95%), vethe degrees of freedom for pooled error, Vep the pooled error variance, r the sample size for the confirma-tion experiment, and neffthe effective sample size.
neff5 N 1 1 DOFopt
ð4Þ
where N is the total number of trials and DOFoptthe total degrees of freedom associated with items used in the hopt esti-mate. With a CI of 95% for the tensile shear strength, the F0.005;1;6 5 5.99, and Vep 5 0.448, the sample size for the confirmation experiment r is 2, N 5 16, DOFopt 5 9, and the effective sample size neff1.6. Thus, the CI is computed to be 1.738 (dB). The experimental results (Table 7) confirm that the initial optimizations of the RSW process parameters (Af3mmB11,000AC1.8kND20cycles) were achieved.
Although the conformity of reproducibility for the experimen-tal results has been confirmed with an average tensile shear strength of specimens as high as up to 4.406 kN obtained, however, a phenomenon of spark was taken place between
Table 4—Summary of experiment data*
TRIAL NO.
CONTROL FACTORS TENSILE SHEAR STRENGTH A B C D AVERAGE (kN) SNR (dB) 1 1 1 1 1 3.317 10.41 2 1 2 2 2 4.098 12.25 3 1 3 3 3 4.105 12.26 4 1 4 4 4 4.392 12.85 5 2 1 2 3 3.299 10.35 6 2 2 1 4 3.758 11.49 7 2 3 4 1 3.950 11.91 8 2 4 3 2 3.855 11.70 9 3 1 3 4 2.622 8.36 10 3 2 4 3 3.735 11.44 11 3 3 1 2 4.168 12.39 12 3 4 2 1 4.083 12.22 13 4 1 4 2 2.318 7.29 14 4 2 3 1 3.572 11.05 15 4 3 2 4 3.637 11.21 16 4 4 1 3 4.139 12.24
*Total average of SNR for all trial hˆ is 11.213 (dB).
Table 5—SNR response table for the tensile
shear strength
FACTOR
PROCESS
PARAMETER LEVEL 1 LEVEL 2 LEVEL 3 LEVEL 4
A The size of electrode tip 11.941 11.363 11.101 10.449 B Welding current 9.102 11.558 11.942 12.252 C Electrode force 11.634 11.507 10.842 10.871 D Welding time 11.399 10.905 11.571 10.979
the specimens and the electrode during the spot welding pro-cess that leads to a severely shortened life cycle of electrode and a collaterally affected joint quality of weldment for its subsequent welding. With the ANOVA outcomes (Table 6) referenced, a proper regulation of welding current is neces-sary to cope with the foregoing defects. As learned from Fig. 2 (SNR graph), SNR thereof was slightly increased when weld-ing current regulated from 7800 A to 11,000 A, that is, the tensile shear strength of specimens was not heightened in big magnitude. Therefore, the optimal conditions of parameters obtained from the application of the Taguchi method remained unchanged except the welding current was regulated from 11,000 A to 7800 A. Table 8 lists the results of experiment after adjusting the parameters (Af3mmB7800AC1.8kND20cycles).
LEVENBERG–MARQUARDT BP ALGORITHM
NNs are to be used for modeling of complex manufacturing processes, usually with regard to process and quality con-trol.13,14 Several well-known supervised learning networks use a BP NN. Funahashi15 proved that the BP NN may approximately realize any continuous mapping. BP learning employs a gradient-descent algorithm to minimize the mean square error (MSE) between the target data and the predic-tions of an NN. However, one of the major problems with conventional BP algorithm (gradient-descent algorithm) is the extended training time required. The techniques for accel-erating convergence have fallen into two main categories: heuristic methods and standard numerical optimization methods such as the LMBP algorithm.16
The LMBP algorithm is similar to the quasi-Newton method, in which a simplified form of the Hessian matrix (second
derivatives) is used. When the cost function has the form of a sum of squares, then the Hessian matrix H can be approx-imated as:
H 5 JTJ ð5Þ
And the gradient g can be computed as:
g 5 JTe ð6Þ
where J is the Jacobian matrix that contains first derivatives of the network errors with respect to the weights and biases, and e a vector of network errors. The Jacobian matrix can be computed through a standard BP technique that is much less complex than computing the Hessian matrix.17
An iteration of this algorithm can be written as:
XK115 XK2½JTJ 1 mI2 1JTe ð7Þ when the scalar m is zero, this is just Gauss–Newton, using the approximate Hessian matrix. When m is large, this becomes gradient descent with a small step size.
The algorithm begins with m set to some small value (e.g., m 5 0.01). If a step does not yield a smaller value for e, then the step is repeated with m multiplied by some factor u . 1 (e.g., u 5 10). Eventually, e should be decreased since we would be taking a small step in the direction of steepest descent. If
Table 8—Results of the Taguchi method with proper
regulation
TRIAL NO.
TENSILE SHEAR STRENGTH
AVERAGE (kN) N1 SPECIMENS N2 SPECIMENS 19 4.089 3.945 3.926 3.731 3.851 N1 5 3:988 N2 5 3:713 20 3.878 4.041 3.585 3.611
Table 6—Results of ANOVA for the tensile shear strength
FACTOR
DEGREE OF
FREEDOM SUM OF SQUARE MEAN SQUARE F TEST
PURE SUM OF SQUARE PERCENT CONTRIBUTION A 3 4.599 1.533 3.42 3.25 9.54 B 3 24.748 8.249 18.40 23.40 68.61 C 3 2.071 0.690 1.54 0.73 2.13 D 3 1.248* Error 3 1.442 Error(pooled) (6) (2.691) (0.448) 6.15 19.72 Total 15 34.109 34.229 100
*The factors are treated as pooled error.
Table 7—Results of the confirmation experiment
TRIAL NO.
TENSILE SHEAR STRENGTH
CI (95%) N1 SPECIMENS N2 SPECIMENS SNR (dB) AVERAGE (kN) 17 4.562 4.505 4.335 4.209 12.861 4.406 12.98 ± 1.74 (dB) 18 4.426 4.343 4.626 4.243 12.875
a step does produce a smaller value for e, then m is divided by u for the next step, ensuring that the algorithm will approach Gauss–Newton, which should provide faster convergence.16 The LMBP algorithm is the fastest algorithm that has been tested for training multiplayer networks of moderate size, even though it requires a matrix inversion at each iteration. It requires two parameters, but the algorithm does not appear to be sensitive to this selection.
TRAINING OF BP NETWORK
Multilayer feedforward NNs are commonly used for solving difficult predictive modeling problems.18They usually consist of an input layer, one or more hidden layers, and one output layer. The neurons in the hidden layers are computational units that perform nonlinear mapping between inputs and outputs. A feedforward NN was used in this study. It takes a set of five input values (control factors A, B, C, D, and noise factor) and predicts the value of one output (tensile shear
strength of the specimens). The transfer functions for all hid-den neurons are tangent sigmoid functions and a linear func-tion is used for the output neurons.19 Determining the number of hidden neurons is critical in the design of NNs. An overabundance of hidden neurons give too much flexibility that usually leads to overfitting. On the other hand, too few hidden neurons restrict the learning capability of a network and degrade its approximation performance.18 A total of 64 input–output data patterns were partitioned into a training set, a testing set, and a validating set. Functionally, 60% (38 patterns) were randomly selected for training the NN, while the remaining 20% (13 patterns) were randomly selected for testing and 20% (13 patterns) randomly selected for validat-ing. An efficient algorithm, the Levenberg–Marquardt algo-rithm, was used to improve classical BP learning in the training process.17,19The performance of each NN was mea-sured with the MSE of the testing subset. Table 9 presents nine options for the NN architecture. After comparing all the data for the MSE value, the structures 5-4-1, 5-5-1, 5-7-1, 5-8-1, and 5-9-1 are the five best convergence criteria. The structure 5-7-1 showed the least simulating error and was
Table 9—Options for different networks
ARCHITECTURE (INPUT-HIDDEN UNIT-OUTPUT) MEAN SQUARE ERROR FOR TRAINING RANK OF MSE SIMULATING ERROR, % (COMPARE WITH AVERAGE VALUE IN TABLE 8) N1 SPECIMENS N2 SPECIMENS 5-2-1 0.1123 5-3-1 0.1083 5-4-1 0.0337 5 23.81 1.85 5-5-1 0.0282 4 20.98 6.19 5-6-1 0.2383 5-7-1 0.0147 2 3.50 20.54 5-8-1 0.0096 1 27.92 26.28 5-9-1 0.0194 3 24.93 2.36 5-10-1 0.0490
Fig. 3: The BP network topology of the RSW process Fig. 5: Results of simulating different electrode force Fig. 4: Results of simulating different welding time
therefore selected to obtain a better performance. The topol-ogy of the network 5-7-1 with a m value of 0.001 and a u value of 10 is shown in Fig. 3.
Simulation with a Well-Trained Network
The control factor D (welding time) is the insignificant weld-ing parameters in affectweld-ing the quality characteristic as shown in Table 6. First, the trained network 5-7-1 with 1.47% MSE was employed as the simulating function of the insignificant parameters in this welding process. In Figs. 4–7, the N1 specimens (without any cleaning treatment) had sim-ulated with 0% cleanliness and the N2 specimens (cleaned with acetone) had simulated with 100% cleanliness. Figure 4 shows the comparison of simulating results using the factor D (other conditions Af3mmB7800AC1.8kN), from which it can be seen that the tensile shear strength of specimens is best for adjusting welding time to 15 cycles. Second, Fig. 5 shows the comparison of simulating results using the factor C (other conditions Af3mmB7800AD15cycles), from which it can be seen that the tensile shear strength of specimens is best for setting electrode force at 3.0 kN. Third, Fig. 6 shows the comparison of simulating results using the factor A (other conditions
B7800AC3.0kND15cycles), from which it can be seen that the ten-sile shear strength of specimens is best for setting the size of the electrode tip at f3 mm. Finally, Fig. 7 shows the compar-ison of simulating results using the factor B (other conditions Af3mmC3.0kND15cycles), from which it can be seen that welding current and average tensile shear strength are in direct ratio until about 8200 A. The welding current of RSW process for the initial condition is 7800 A. Therefore, the welding current at 7800 A has been selected in this study.
Experimental Results of Proposed Approach
With combination of this Taguchi method and an NN, the optimal welding conditions for tensile shear strength with RSW process were electrode tip size at f3 mm, welding cur-rent at 7800 A, electrode force at 3.0 kN, and welding time at 15 cycles. Table 10 shows the experimental results obtained with above optimal welding parameters. Table 11 shows the experimental results with the conditions of production opera-tion currently (Af4mmB7800AC1.8kND8cycles). Comparison of Table 8 with Table 11 shows that the increase in average ten-sile shear strength from the initial conditions to the initial optimal parameters (apply the Taguchi method only) is 0.309 kN. Comparison of Table 10 with Table 11 shows that the increase in average tensile shear strength from the initial conditions to the real optimal parameters (apply the Taguchi method and NN) is 0.566 kN. The surface condition of speci-mens for different parameters is shown in Fig. 8. In summary, the quality of RSW process for high-strength steel sheet can be efficiently improved with the proposed approach.
CONCLUSIONS
(1) The improvement of the average tensile shear strength from initial conditions to the initial optimal parame-ters (apply the Taguchi method only) is about 8.72%. The improvement of the average tensile shear strength from initial conditions to the real optimal parameters (apply proposed approach) is about 15.98%.
(2) The proposed approach is relatively effective and easy for engineers to apply to a range of other processes. In addition, applying the proposed approach allows Fig. 6: Results of simulating different size of the electrode tip
Fig. 7: Results of simulating different welding current
Table 10—Results of the proposed approach
TRIAL NO.
TENSILE SHEAR STRENGTH
AVERAGE (kN) N1 SPECIMENS N2 SPECIMENS 21 4.310 4.169 4.112 3.746 4.108 22 4.153 3.973 4.522 3.876
Table 11—Results of the initial conditions
TRIAL NO.
TENSILE SHEAR STRENGTH
AVERAGE (kN) N1 SPECIMENS N2 SPECIMENS
23 3.329 3.518 3.605 3.344 3.542
engineers to directly use NN software to optimize the parameters without any theoretical knowledge of neu-ral computing.
ACKNOWLEDGMENT
The authors acknowledge Mr. Liang-Wei Gao, the engineer of the Production Engineering Division of China Motor Co., Ltd., Taiwan, for permitting the use of the resistance spot welder in this study.
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n
Fig. 8: Surface conditions of specimens for validating the proposed approach: (a) initial conditions, (b) apply the Taguchi method only, (c) apply the Taguchi method with proper regulation, and (d) apply proposed approach
