## 3 Results
### ANFIS Performance Results  
In this study, the ANFIS model was applied for current estimation. It was observed that ANFIS models have demonstrated effectiveness in various applications by combining the learning capabilities of ANN with the reasoning abilities of fuzzy logic [31; 32; 33; 34; 35; 36; 37; 38]. Figures 6 and 7 show the fuzzy inference system (FIS) model and the structure of ANFIS model, respectively. In Figure 7, the logical operations in the ANFIS model are shown as blue (AND operation), red (OR operation), and green (NOT operation). However, only the AND operation is used in the designed ANFIS model. The parameters were determined as 30 training cycles, 200 membership functions, and \"gbellmf\"-type membership function in ANFIS model. A total of 200 ANFIS rules were created within the scope of the study. Figure 5: Performance analysis of the shifted filtered current signal (SFCS) and filtered arc light signal (FALS) for the 3.25 mm and 2.50 mm electrodes: (**a**) FALS and filtered current signal (FCS) for the 3.25 mm electrode; (**b**) FALS and SFCS for the 3.25 mm electrode; (**c**) FALS and FCS for the 2.50 mm electrode; (**d**) FALS and SFCS for the 2.50 mm electrode. Note: FCS, filtered current signal; SFCS, shifted filtered current signal; FALS, filtered arc light signal. Figure 6: Generated FIS models. Different experiments were performed for each average level (140 A, 120 A, 100 A and 80 A), and the data obtained were combined to form training and test sets. The training and test results of the experiments with electrodes of 3.25 mm in diameter are presented in Figure 8 and Figure 10, respectively; also, the same was done for the 2.50 mm diameter electrode shown in Figure 9 and Figure 11.  
Analysis of the data presented in Figure 8a reveals a strong overall agreement between FSACO and the target FCS. However, the same figure also indicates a degree of lag and some deviations in FSACO's response to abrupt changes in the FCS. A similar trend is observed in Figure 9a. The sharp peaks shown in the cross-correlation graphs in Figures 8b and 9b indicate that FSACO's with diameters of 3.25 mm and 2.50 mm effectively follow the FCS. Figure 8: Performance analysis of the ANFIS model with training data for the 3.25 mm electrode: (**a**) comparison of filtered shifted ANFIS current output (FSACO) with the target FCS; (**b**) cross-correlation between the target FCS and FSACO; (**c**) comparison of FALS and FSACO. Note: FSACO, filtered shifted ANFIS current output. Figure 7: The structure of ANFIS model. As a result of the performance metrics calculations, regarding the data presented in Figure 8a, the R-squared value between the FSACO and the target FCS was calculated as 0.7033, and the RMSE value was 32.6174 A. According to the data in Figure 8b, the maximum cross-correlation value between the FSACO and the target FCS was determined as 0.9587, and the comparison of the FSACO and the FALS is presented in Figure 8c. Similarly, according to the data presented in Figure 9a, the R-squared value was calculated as 0.7640 and the RMSE value as 29.4357 A. In Figure 9b, the maximum cross-correlation value was found to be 0.9598. The data presented in Figure 9c show the relationship between FSACO and FALS. In Figure 8c, it is observed that FSACO responds to the gradual increase and decrease behaviors of FALS, which are based on the movements of the welder, and follows FALS in harmony. However, in Figure 8a, it is observed that the welding current FCS cannot respond at the same speed to the sharp changes in FALS corresponding to the welder's sudden movements. A similar trend is observed in Figure 9a. These results reveal that the ANFIS model can be successfully applied on the training data and accurately capture the real current signal. In Figures 10 and 11, it is observed that the models produce consistent estimations at consistent current levels. In Figure 10a, FSACO exhibits a more stable performance at high current levels, while significant deviations occur at low currents and current changes.