Post Processing

Custom-written software (Matlab™, The Mathworks Natick, MA, USA) converted the raw voltage data from the gauges and the accelerometer into impact force and strain data (see Appendix C). The strain data was then further processed with a customized discrete fourier transformation (DFT) code to obtain frequency domain behaviour of each impact. This process along with a representative sample of the strain gauge data and associated frequency spectra is illustrated in Figure 3.1. Each individual impact trial was analyzed manually to extract both the frequency values of each impact and the magnitude of that frequency component (the power).

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Figure 3.1: Strain gauge data in the temporal (top) and frequency (bottom) domain. A DFT was used to tranform the former to the latter.

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The identification of all natural frequencies of a specimen from the combined strain gauge data was complicated by the fact that, depending on their location, different strain gauges may detect none, one or multiple non-consecutive resonant frequencies. Therefore, the resonant fre- quencies of all heights and sites were aggregated for each specimen and analysed with a cluster analysis and 2-way analysis of variance (ANOVA) tests to identify the resonant frequencies of each specimen as well as to compare the effect of heights and sites on the frequencies found. The cluster analysis used is an agglomerative hierarchical technique (Lance and Williams, 1967) which identifies groups of data based on a Euclidean distance proximity matrix and an average between groups linkage criteria. This method allowed us to determine the approximate number of resonant frequencies for each specimen, as well as classify each data-point as part of a distinct resonant frequency. Section 1.5.3 explains cluster analysis techniques in more detail and Figure 3.2 illustrates the effect of this technique for specimen 1652. The cluster analysis was necessary for the following steps in our procedure

Firstly, it was used to compare the sequence of resonant frequencies of each skull. A 1-way ANOVA was used to test the effect of this final variable of specimen on the frequency response of the human skull.

Secondly, with resonant frequency ranges identified for each specimen, the frequencies excited by each gauge to evaluate the gauge specific repeatability were re-examined. Each numerical frequency value excited in a gauge was binned as a resonant frequency according to the ranges identified by the cluster analysis and was then compared to other trials of the same gauge. A binary condition was assigned to each gauge to describe matching frequencies between trials, heights and impact sites. 1 recorded a match and 0 recorded a mismatch. In this way, the consistency of each gauge at exposing particular frequencies with changing impact conditions was evaluated. This also allowed the evaluation of our cluster analysis technique and modify cluster groups if necessary. Specifically if two or more recorded frequencies at a single gauge belonged in the range of only one frequency according to the cluster analysis, the cluster analysis was modified to split that bin to distinguish between the two separate frequencies

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Figure 3.2: Effect of cluster analysis for specimen 1652. Each data point represents a frequency value extracted from one of the gauge frequency spectra. The cluster analysis algorithmically determines groups in the linear data, clumping all similar frequency values in the same cluster. Each cluster is then identified as a different resonant frequency, with each data point of that cluster representing a sample exposing that frequency.

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identified by the gauge.

The effect of height, site and specimen on the powers of each resonant frequency was analyzed by comparing the ratios of these powers for each frequency. To do this, the power of each resonant frequency evident in each trial was recorded. As it was typical for a single gauge to record only a few of the possible resonant frequencies (as per the cluster analysis) a 0 power was assigned to the cases were a particular resonant frequency was not exposed by the gauge for a particular trial. This allowed us to take a weighted average of each resonant frequency and calculate it as a ratio of all resonant frequencies possible. A ratio of each resonant frequency was calculated for the total of all hight/site combinations, as well as for the total of all sites for a particular height, and of all heights for a particular site. The power ratio was also taken for individual height/site combinations and compared to establish the effect of height, site and specimen on the power ratio of the frequency spectra.