A BFGS and simple step method for estimating the interface temperature in 2D ultrasonic seam welding

An inverse method for estimating unknown interface heat generation in an ultrasonic seam welding process based on a combination of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) and Simple Step Method is presented. In this study, a nonlinear direct problem is solved by using the Hybrid Spline Difference Method (HSDM). Heat generation and interface temperature, which are extremely difficult to directly measure, can be determined inversely through the Direct Problem, Adjoint Problem, and the Simple Step Method without sensitivity analysis. Special features of proposed method are stable, accurate, and efficient for estimating moving heat sources and interface temperature even including measurement error. The predicted interface heat generation and temperatures are in very good agreement with exact solutions for different heat sources profiles. Furthermore, the influence of the measurement location on the accuracy of estimated solutions with or without error of measurement was also discussed. These findings indicate that the estimated heat generation is more sensitive than the temperature to different measured errors and locations. According to analysis of results, the occurrence of thermal defects can be avoided during the welding process. In addition, the proposed method strongly provides good information for optimization of the welding process.