HSDM and BFGS method for determining the heat generation and range of heat distribution in 2-D ultrasonic seam welding problems

ABSTRACT

An inverse method based on the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method and the simple step method is proposed to estimate unknown heat generation at the welding interface during actual ultrasonic seam welding with knowledge of temperatures taken in a workpiece. The efficiency of the hybrid spline difference method (HSDM) compared to the finite-difference method (FDM) is presented. In addition, a comparison of the BFGS method and the conjugate gradient method (CGM) is made. Results show that the estimated temperature is in very good agreement with the measurement temperature. In addition, the heat generation and its distributed range are predicted rapidly. According to the analysis results, the proposed method is an accurate, robust, and efficient method for the prediction of temperature and moving heat generation in an ultrasonic welding process.