Modified Dynamic Time Warping for Utilizing Partial Curve Data to Calibrate Material Models

Material calibration can be solved as a non-linear regression problem in which a parametric model of the material test is calibrated to its experimental result. In typical material testing, temporal and/or spatial data is produced experimentally and compared to its computational equivalent. At its basic level a single response comparison consists of two curves which are matched to produce a distance between them. The calibration requires minimizing the distance measure. The difficulty of the comparison is determined by phenomena such as noise, hysteresis and differences in geometric curve length (length compatibility). While noise and hysteresis problems have been solved in this context using LS-OPT® in the distant past, the question of curves having substantially different lengths has remained a challenge until recently. In one example, the computational output extracted from LS-DYNA® causes parts of the output to not be relevant to the test data. In this case most distance measures produce spurious distance calculations. This paper introduces a method to address this question. The approach is based on a modification of the Dynamic Time Warping distance measure and referred to as Modified Dynamic Time Warping or DTW-p (for partial). It consists of the trimming of the DTW path as well as iterative mapping to produce a uniform map. An example based on output of the GISSMO model in LS-DYNA is used to demonstrate the effectiveness of the method.