1 Erratum to: Appl. Phys. A DOI 10.1007/s00339-015-9408-5

The original version of this article unfortunately contained mistakes.

The presentation of Fig. 12 and Table 9 was incorrect. A sentence in Sect. 4.1 showed wrong data. The correct Fig. 12 and Table 9, and sentence are given below.

Fig. 12
figure 12

The cross section of the weld seam generated by optimized parameters

Table 9 Confirmation test results

From Table 9, the optimal F is 232.041, and the corresponding feasible solution value is 235.35, and the error between them is −1.43 %.

The original article was corrected.