Predicting RMS surface roughness using fractal dimension and PSD parameters

Off-road vehicle performance is, in part, related to the ride comfort of the vehicle while operating on rough terrain. The surface undulations altering vehicle ride over homogeneous areas are defined, by the US Army, as a single number descriptor entitled root-mean-square (RMS). A current need exists to attribute large geographic areas with RMS values in order to better support vehicle speed predictions with remotely sensed data. The RMS is typically computed using centimeter scale data, which can be difficult and time consuming to collect. A technique to extrapolate RMS for large areas was developed based on meter-scale data to predict RMS using a combination of fractal dimension and spectral analysis. Validation of the extrapolation technique was based on 43 vehicle ride courses with 30-cm data. For each ride course, a two dimensional fractal dimension (FD) was computed using the divider method, and a discrete Fourier transform (DFT) was used to compute the power spectral density (PSD). A regression analysis was performed to search for correlations between RMS, FD, and PSD given fixed-slope power law fit parameters. Using a stepwise model selection, a statistical model for rapid predictions of RMS was developed. The RMS was computed from FD and the PSD DC offset to within 80% agreement using a linear model.