A modified Newton–Raphson method to estimate the temperature-dependent absorption coefficient in laser welding process.

Estimation of the temperature-dependent absorption coefficient in laser welding process is known as high non-linear inverse problem. Thus, it is necessary to propose a robust and efficiency method to estimate this coefficient. In this paper, a modified Newton–Raphson method combined with the concept of future time is presented to estimate the absorption coefficient in the laser welding process. The special characteristics of this method are that no preselected functional form for the unknown absorption coefficient is necessary and non-linear least-squares is not needed in the algorithm. Two examples have been fulfilled to demonstrate the proposed method. The results show that the proposed method is an accurate, stable, and efficient method to estimate the absorption coefficient in the laser welding process. In addition, two kinds of future time description are considered in this work. One is a linear type and the other is a constant type. From the estimated results, it is evidenced that the accuracy of the estimated results for the linear type of future time description is higher than that for the constant one of future time description. [ABSTRACT FROM AUTHOR]