A B C Discussion and Validation The linear model in Equation 6A accounts for the average of the nonlinear human welder’s response in the operation range of the parameters used to conduct the dynamic experiments. Specifically, the coefficient for the width is –0.16, indicating the average negative effect of the width on the current adjustment. The coefficient for the length is 0.08. This implies that the skilled welder treats width more importantly than the length, given the magnitude of the width and length are similar. For the weld pool convexity, the coefficient is 1.81. This implies that in general the human welder increases the current if the convexity is increased. The coefficient for the previous adjustment (0.26) indicates that the human welder adjustment at current instant also correlates to the previous adjustment, and the correlation is positive. One may think that the model improvement from Table 5 (4 to 7% for three criteria proposed in this study) is not significant. However, the ANFIS model is derived in analytical form and can be implemented in real time. The resultant model improvement is achieved at no additional costs. In addition, the human welder response is better modeled and understood. In this sense, the proposed ANFIS model is considered a better way to represent the intrinsic nonlinear and fuzzy inference a human welder possesses. In addition, Fig. 12 shows a detailed view of the modeling result comparison between the linear model and ANFIS model from sample number 0 to 180, 480 to 620, and 1350 to 1460, respectively. It is observed that noticeable improvements are made by the proposed ANFIS model. Although the linear model analysis can reveal some information about skilled welder’s adjustments, detailed information is lost because of the incapability of the linear modeling, which can only model the average effect of the input parameters over the output. The nonlinear ANFIS model, however, can discover detailed information about the human welder intelligence. Because of the relative complexity of the ANFIS model, its analysis will be more comprehensive. Hence, the ANFIS model will be analyzed and compared with that of the novice welder in a following investigation. To further verify the skilled human welder model, verification experiments WELDING JOURNAL 51-s WELDING RESEARCH Fig. 12 — Model comparison between linear and ANFIS model. Table 4 — Identified 16 Neuro-Fuzzy Model Rules with Four Inputs Rule IF THEN (Skilled Welder) (1,1,1,1) P1 is narrow, P2 is short, y(1,1,1,1) = 5.87p1 + 1.575p2 P3 is small, and P4 is small –79.03p3 - 2.424p4 - 7.464 (1,1,1,2) P1 is narrow, P2 is short y(1,1,1,2) = -8.68p1 – 2.08p2 P3 is small, and P4 is large +156.2p3 -1.5p4 + 8.31 (1,1,2,1) P1 is narrow, P2 is short y(1,1,2,1) = 0.338p1 – 0.782p2 P3 is large, and P4 is small +47.85p3 + 1.56p4 – 5.91 (1,1,2,2) P1 is narrow, P2 is short y(1,1,2,2) = - 2.429p1 + 1.33p2 P3 is large, and P4 large – 59.76p3 - 1.63p4 + 8.49 (1,2,1,1) P1 is narrow, P2 is long y(1,2,1,1) = – 3.05p1 + 7.547p2 P3 is small, and P4 is small + 443.8p3 + 14.46p4 – 65.44 (1,2,1,2) P1 is narrow, P2 is long y(1,2,1,2) = - 1.563p1 – 0.592p2 P3 is small, and P4 is large – 395.2p3 + 8.146p4 + 32.86 (1,2,2,1) P1 is narrow, P2 is long y(1,2,2,1) = 1.934p1 + 2.46p2 P3 is large, and P4 is small + 189.8p3 - 2.985p4 - 59.65 (1,2,2,2) P1 is narrow, P2 is long y(1,2,2,2) = - 7.64p1 – 3.43p2 P3 is large, and P4 is large – 80.49p3 + 0.4699p4 + 60.33 (2,1,1,1) P1 is wide, P2 is short y(2,1,1,1) = 2.05p1 + 2.8p2 P3 is small, and P4 is small – 48.32p3 + 3.61p4 – 10.93 (2,1,1,2) P1 is wide, P2 is short y(2,1,1,2) = - 4.77p1 + 4.22p2 P3 is small, and P4 is large + 33.41p3 + 4.573p4 + 3.56 (2,1,2,1) P1 is wide, P2 is short y(2,1,2,1) = - 1.65p1 + 0.92p2 P3 is large, and P4 is small – 77.76p3 + 0.1138p4 + 20.2 (2,1,2,2) P1 is wide, P2 is short y(2,1,2,2) = - 2.46p1 + 0.03p2 P3 is large, and P4 is large + 51.38p3 + 1.148p4 + 1.568 (2,2,1,1) P1 is wide, P2 is long y(2,2,1,1) = - 2.01p1 – 0.994p2 P3 is small, and P4 is small – 37.44p3 - 1.534p4 + 17.09 (2,2,1,2) P1 is wide, P2 is long y(2,2,1,2) = 3.36p1 + 1.763p2 P3 is small, and P4 is large + 22.88p3 – 2.229p4 – 30.32 (2,2,2,1) P1 is wide, P2 is long y(2,2,2,1) = 0.34p1 – 0.003p2 P3 is large, and P4 is small – 7.404p3 + 0.3415p4 – 2.028 (2,2,2,2) P1 is wide, P2 is long y(2,2,2,2) = – 1.12p1 – 0.141p2 P3 is large, and P4 is large – 11.77p3 - 0.1821p4 + 12.62 Table 5 — Model Comparison between Neuro-Fuzzy Model and Linear Model Average Model Error/A RMSE/A Maximum Model Error/A Linear Model 0.52 0.79 3.15 ANFIS Model 0.50 0.76 3.03
Welding Journal | February 2014
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