Identification of welding residual stress of butt-welded plate using the boundary element inverse analysis with Tikhonov's regularization

This paper deals with an inverse problem for estimating the magnitude of the residual stress in a butt-welded plate from measured data. The welding residual stresses in the butt-welded plate are caused by inherent strain. Thus, the welding residual stress in the butt-welded plate can be calculated if the inherent strains are estimated from measurement data. In previous works, a method was proposed to estimate the inherent strains in the butt-welded plate using thermo-elastic boundary element inverse analysis. It was found in the paper that the evaluated value of the inherent strains in the butt-welded plate depended on the location or the number of measurement points in the butt-welded plate. The accuracy of the evaluated inherent strains was low when the location of the measurement point was far from the welding line and the number of measurement points was small. Thus, this paper uses Tikhonov's regularization to improve the accuracy of the evaluated values of the inherent strains in the butt-welded plate. Numerical simulations were conducted for an analysis model which was the same with that used in the previous paper. In the simulations, measurement errors were included in stresses at measurement points. The maximum value of the error was 4.9 (MPa). The results of the calculations showed that the inherent strains in the butt-welded plate were evaluated in high accuracy from a few measured data by using Tikhonov's regularization. The discrepancy principle was applied for estimating a proper value of the regularization parameter. It was found that Tikhonov's method with the discrepancy principle was useful in evaluating the residual stress in the butt-welded plate.