A minimum area discrepancy method (MADM) for force displacement response correlation

With the increasing use of Computer Aided Engineering, it has become vital to be able to evaluate the accuracy of numerical models. Specific methods such as CORA were developed to objectively evaluate the correlation between a physical test and a numerical simulation results in terms of parameter vs time. However, no metric has so far been developed for Force Vs Deflection (FvD) signals often used in crashworthiness and biomechanics. A unique method called the Minimum Area Discrepancy Method, or MADM, is proposed to address this deficiency. This new method initially calculates a parameter 'R' which represents the area between numerical model and the average physical test response and then divides it by the average area generated by the upper and lower test corridors, based on the same standard deviation. The parameter 'R' is then normalized between 0 (no correlation) and 1 (perfect correlation) to become the MADM correlation rating. The MADM method was then validated by comparing a one dimensional Finite Element (FE) model of a chest model, under 2 impact velocities, against reference Post Mortem Human Subject (PMHS) data. The MADM method was further used to improve the correlation of this thorax model, by varying model parameters and generating 81 model variations. Based on the MADM ratings, a set parameter values leading to the best fit was identified. The best fit exhibits a response significantly better than the original chest model. MADM is novel, unique, easy to use and fulfills an important gap in objectively evaluating FVD correlation responses. Abbreviations MADM Correlation rating value (Minimum Area Discrepancy Method) MADM_n,m MADM correlation rating using a specific scaling value of 'n' and power rating 'm' FvD Force versus Displacement FvT Force versus Time DvT Displacement versus Time NM Numerical model PE Physical Experiment A_model Area under the average signal and the Numerical Model A_upper Area under the average signal +1 standard deviation A_lower Area under the average signal -1 standard deviation R Ratio between A_model and the average of A_upper and A_lower.