Modeling Indirect Statistics of Surface Roughness

AR(1) time series with autoregressive gamma variance for road topography modeling

“…The method is based on the equations (11) and (17). The formula for the one lag autocorrelation of Y can be used to establish a relation between ρ x and ρ r .…”

“…Consequently, we have the possibility of using (17) to match ρ r with the empirical evidence, by replacing ρ y 2 by the standard sample estimate of the autocorrelation of the squared values of the signal. Then, using the right hand side of (17), one can use sample estimatesρ y 2 (k) of ρ y 2 (k) to obtain functions G k (ρ x ), k = 1, . .…”

“…However, the authors of that pioneering paper were aware that Gaussian processes cannot "exactly reproduce the profile of a real road". Although models based on Gaussian distributions are standard in the field (see, e.g., [17] and also [14] for some recent studies), most experts of vehicle engineering agree that road surfaces are not, in fact, accurately represented by a Gaussian distribution. One reason for this is that the actual roads contain short sections with above-average irregularity.…”

Laplace distribution models for road topography and roughness

“…Direct Gaussian models are convenient since linear filter responses are Gaussian processes as well. Although models based on Gaussian distributions are standard in the field, see, for example, (Sun et al, 2001;Múčka, 2004) for some recent studies, most experts of vehicle engineering agree that road surfaces are not, in fact, accurately represented by a Gaussian distribution, see (Dodds & Robson, 1973). One reason for this is that the actual roads contain short sections with above-average irregularity.…”

“…Top graph has independent random factors (a r = 0) and the bottom graph has correlated AR(1) factors with a r = 0.9. for waviness w = 2, 2.5, respectively, where the roughness coefficient C has units m 3 /rad. The theoretically derived relationship between IRI and C can be generalized to arbitrary waviness and speed, see (Sun et al, 2001), (Johannesson & Rychlik, 2014), and (Kropáč & Múčka, 2004& Múčka, , 2007. For completeness, we give formulas to estimate the parameter C in the ISO spectrum (13) if the IRI value is known, viz.…”