Comments on Kurtosis of Military Vehicle Vibration Data

Abstract

Road vibration tests were recently conducted on a series of shelters on dolly sets and on a series of prototype trucks at the U.S. Army Combat Systems Test Activity (USACSTA) at Aberdeen Proving Ground. Data from histogram or amplitude distribution tables were plotted in the normal probability domain to provide a graphic representation. When examining these probability plot data, a divergence of the actual distribution from the normal distribution at the tails was noticed. Of the 104 trials compared, the normal distribution was exceeded by 30 trials at the 90 percent level, 87 trials at the 99 percent level, and 88 trials at the 99.9 percent level. This indicates that the actual measured values at the extreme ends of the distribution (beyond the 90 percent occurrence levels) are larger in magnitude (acceleration) than would be predicted by the assumption of a normal distribution. This same trend was noticed during examination of the kurtosis values for the same data sets. The values generally exceeded a value of three, which is the expected value for a Gaussian distribution. Because the kurtosis is largely affected by data values far from the mean, a correlation between the normalized 99.9 percent values and the normalized kurtosis values was tried. A linear regression line was fit through the data, which produced a correlation of approximately 0.82. Although no formal effort has been put forth to catalog kurtosis measurements from military vehicles, it has generally been observed that the kurtosis values obtained from operation over our test courses is greater than three, indicating that the tails of a vibration distribution from operation over severe terrain are further from the mean (larger amplitude) than would be predicted from a normal distribution. If the kurtosis of the laboratory test distribution is less than that of the field distribution, the extreme values seen in the field environment will not be duplicated in the lab. The addition of conservatism during the schedule development process should be enough to overcome this difference; however, dome effort should be made to develop a "bi-domain" (frequency and time domain amplitude) control system so that the amplitude distribution of the lab test will more closely match that of the field data from which the schedule was derived.