Welding residual stress estimation from surface stress using gappy proper orthogonal decomposition

Understanding residual stress induced by welding continues to be an essential issue for joint design and product performance assessment. We propose a method to evaluate internal stress distributions from surface stresses using gappy proper orthogonal decomposition (POD). The POD modes were constructed by singular value decomposition of stress data (i.e., snapshot data for a one-pass bead-on-plate model with various heat inputs) calculated from a thermo-elastoplastic finite element analysis. The POD mode coefficients were calculated by a linear inverse problem with a regularization term using the surface stress data at the locations determined by the greedy algorithm. As a result, even when the surface stress contained noise with a standard deviation of 5 % of the maximum stress, the mean absolute error of the stress was less than 20 MPa, indicating stable estimation. By combining the proposed method with X-ray diffraction technique, a surface stress measurement method, the welding process is expected to be monitored and evaluated with a focus on internal stress.