An improved method for obtaining rotational accelerations from instrumented headforms

Abstract

The following compares the effect of differentiation methods used to acquire angular acceleration from three types of un-helmeted headform impact tests. The differentiation methods considered were the commonly used 5-point stencil method and a total variation regularization method. Both methods were used to obtain angular acceleration by differentiating angular velocity measured by three angular rate sensors (gyroscopes), and a reference angular acceleration signal was obtained from an array of nine linear accelerometers (that do not require differentiation to obtain angular acceleration). For each impact, three injury criteria that use angular acceleration as an input were calculated from the three angular acceleration signals. The effect of the differentiation methods were considered by comparing the criteria values obtained from gyroscope data to those obtained from the reference signal. Agreement with reference values was observed to be greater for the TV method when a user-defined tuning parameter was optimized for the impact test and cutoff frequency of each condition, particularly at higher cutoff frequencies. In this case, mean absolute error of the five-point stencil ranged from 1.0 (the same) to 11.4 times larger than that associated with the TV method. When a constant tuning parameter value was used across all impacts and cutoff frequencies considered in this study, the TV method still provided a significant improvement over the 5-point stencil method, achieving mean absolute errors as low as one-tenth that observed for the five-point stencil method.